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Isotropic Compliance in E(3): Feasibility and Workspace Mapping
Abstract
A manipulator control system, for which isotropic compliance holds in the Euclidean space E(3), can be significantly simplified by means of diagonal decoupling. However, such simplification may introduce some limits to the region of the workspace where the sought property can be achieved. The present investigation reveals how to detect which peculiar subset, among four different classes, a given manipulator belongs to. The paper also introduces the concept of control gain ratio for each specific single-input/single-output joint control law in order to limit the maximum gain required to achieve the isotropic compliance condition.
... In Ref. [31], conditions required to achieve a special isotropic compliance in a 2D Euclidean space with a serial mechanism with specified link lengths was presented. ...
... (1) Select the location of J 1 . To satisfy inequality (31), the distance between joint J 1 and the compliance center C c must be less than 4 m. Here, J 1 is located at position (3, 3) Transactions of the ASME (inside the rectangle enclosed by the four lines l ± x and l ± y as illustrated in Fig. 9), which satisfies the two lower bound inequalities of (16) and (17). ...
In this article, the synthesis of any specified planar compliance with a serial elastic mechanism having previously determined link lengths is addressed. For a general n-joint serial mechanism, easily assessed necessary conditions on joint locations for the realization of a given compliance are identified. Geometric construction-based synthesis procedures for five-joint and six-joint serial mechanisms having kinematically redundant fixed link lengths are developed. By using these procedures, a given serial manipulator can achieve a large set of different compliant behaviors by using variable stiffness actuation and by adjusting the mechanism configuration.
... Furthermore, a control strategy has been proposed and simulated. As shown in literature [43][44][45], grippers and microgrippers have been extensively developed during the last decades and, more recently, new synthesis techniques [46][47][48][49] allowed designers to handle tissue also by selective, non isotropic compliance [50]. A former version of microgripper for tissue manipulation has been presented in 2015 [51], while this paper presents a new refined version of the hardware and a new control system for measuring both the stiffness and the viscosity coefficient of the tissue sample. ...
... If the input torque is planned by the operator that performs the measurement, the constant value ε has to be fixed in order to guarantee that τ 2 τ 0 2 ; otherwise, if a closed loop control system as in Figure 11 is used, the input referenceθ 4,re f =θ 0 4 + α sin(ωt) (46) must be chosen in order to produce, as gripper input, the torque (43), by setting the value of α suitably. Then, it is possible to evaluate the unknown damping coefficient value c by measuring the amplitude of the steady state sinusoidal behaviour of the ϑ 4 angle after that a sinusoidal exciting torque is applied to the first joint, thanks to the known dependency of M(ω) from the parameter c itself. ...
As many studies show, there is a relation between the tissue’s mechanical characteristics and some specific diseases. Knowing this relationship would help early diagnosis or microsurgery. In this paper, a new method for measuring the viscoelastic properties of soft materials at the microscale is proposed. This approach is based on the adoption of a microsystem whose mechanical structure can be reduced to a compliant four bar linkage where the connecting rod is substituted by the tissue sample. A procedure to identify both stiffness and damping coefficients of the tissue is then applied to the developed hardware. Particularly, stiffness is calculated solving the static equations of the mechanism in a desired configuration, while the damping coefficient is inferred from the dynamic equations, which are written under the hypothesis that the sample tissue is excited by a variable compression force characterized by a suitable wave form. The whole procedure is implemented by making use of a control system.
... The major limitations of using optimization for the realization problem are that: 1) optimization does not ensure that any specified compliance can be achieved even with a large number of redundant joints; 2) the optimal solution may not preserve the desired compliant behavior of the original compliance; and 3) the results obtained from optimization provide little physical insight into the limits of passive compliance realization. In more recent work [22][23][24], the realization of isotropic compliance in the Euclidian spaces E(2) and E(3) with robotic mechanisms has been addressed. Equations relating the Cartesian compliance entries to the joint compliance and the mechanism geometry were developed. ...
... b) If the mechanism is non-Grashof with L 2 being the longest link, then any compliance matrix can be realized. c) If the mechanism satisfies conditions (21)- (22) or conditions (23)- (24), then any compliance can be realized. ...
This paper presents methods for the realization of 2 × 2 translational compliance matrices using serial mechanisms having only revolute joints, each with selectable compliance. The link lengths of the mechanism and the location of the compliant frame relative to the mechanism base are arbitrary but specified. The realizability of a given compliant behavior is investigated, and necessary and sufficient conditions for the realization of a given compliance with a given mechanism are obtained. These realization conditions are interpreted in terms of geometric relationships among the joints. We show that, for an appropriately sized 3R serial mechanism, any single 2 × 2 compliance matrix can be realized by properly choosing the joint compliances and the mechanism configuration. Requirements on mechanism geometry to realize every particle planar elastic behavior at a given location just by changing the mechanism configuration are also identified.
... Barazini (Fig. 3C). During the past several decades, microgrippers have been widely developed, and more recently, novel synthesis techniques [63,64] have allowed designers to handle tissue via selective, non-isotropic compliance [65]. In one study, the authors designed a MEMS microgripper to measure the stiffness of cells to identify early signs of cancer metastasis. ...
Mechanical stimulation has been imposed on living cells using several approaches. Most early investigations were conducted on groups of cells, utilizing techniques such as substrate deformation and flow-induced shear. To investigate the properties of cells individually, many conventional techniques were utilized, such as AFM, optical traps/optical tweezers, magnetic beads, and micropipette aspiration. In specific mechanical interrogations, micro-electro-mechanical systems (MEMS) have been designed to probe single cells in different interrogation modes. To exert loads on the cells, these devices often comprise piezo-electric driven actuators that attach directly to the cell or move a structure on which cells are attached. Uniaxial and biaxial pullers, micropillars, and cantilever beams are examples of MEMS devices. In this review, the methodologies to analyze single cell activity under external loads using microfabricated devices will be examined. We will focus on the mechanical interrogation in three different regimes: compression, traction, and tension, and discuss different microfabricated platforms designed for these purposes.
... A lot of investigations were conducted earlier to enhancing this very important factor. Kumar and Waldron [3] presented an appropriate algorithm for manipulators of at least 3 joints. They presented a specific method to detect which peculiar subset, among four different classes, a given manipulator belongs to. ...
The workspace of any robot can play a big role in accomplishing the required work perfectly. There are many parameters to be considered when designing and optimization workspace for any specific application. In this study, the effect of the flexibility of the revolute joints angle of rotation for PRR-SCARA robot on its workspaces was investigated. The workspace was studied for 13 cases, and in each case, a different range of motion for motors were selected. An optimization was done for the purpose of choosing the best working range for all robot motors. It was found that increasing the motor's working range on the first rotational joint and reducing it for the next joint will lead to improve and increase in the workspace of the robot under study. A mathematical relationship was proposed to calculate the workspace area for SCARA robot in terms of the motors working ranges with an average error of (2.07%).
... In fact, they can reach a given configuration thanks to external forces that can be applied with a high precision to deform the elastic structure, using also a redundant driving strategy. More recently, active compliance [16,17] has been added as a further possibility in design, acting both as a series or in a parallel configuration with passive compliance. ...
This paper presents a new tendon-driven platform with spatial mobility. The system can be obtained as a monolithic structure, and its motion is based on the concept of selective compliance. The latter contributes also to optimizing the use of the material by avoiding parasitic deformations. The presented platform makes use of lumped compliance with three different kinds of elastic joints. An analysis of the platform mobility based on finite element analysis is provided together with an assembly mode analysis of the equivalent pseudo-rigid body mechanism. Surgical operations in laparoscopic environments are the natural fields of applications for this device.
... Fortunately, recent developments in MEMS Technology allows designers to introduce different sorts of micro mechanisms, such as microgrippers [27,28], with multi-hinge and multi-DoF (Degrees of Freedom) properties, and other multi-axes devices [29]. Such opportunity gave rise to the introduction of a design technique based on the rigid-body replacement method [30], which refers to classical issues of mechanism science such as topology [31,32], kinematic synthesis [33][34][35], kinetostatic indexing [36], isotropic compliance [37,38] and parametric design [39,40]. ...
Manipulating micro objects has become an important task in several applications. Actuation is a crucial aspect of micromanipulation because there are physical restrictions which affect actuators’ performances at the micro or nano scale. One way of getting rid of these limitations is the use of an appropriate mechanical structure which enhances the elasticity of the material or provides mechanical advantage. This Special Issue of Actuators, which is dedicated to micromanipulation, offers a contribution to the development of some promising methods to actuate a microsystem for micromanipulation.
... In fact, during the past years, MRD systems design made substantial advances [13]. Moreover, the availability of joints with variable or controllable damping could be used to adjust the behaviour of more complex systems [33] in E(3) [34] or in SE(3) [35] . ...
Magnetorheological (MR) fluids are capable of manifesting a rheological behaviour change by means of a magnetic field application and can be employed in many complex systems in many technical fields. One successful example is their use in the development of dampers: magnetorheological dampers (MRDs) are widespread in vibration control systems, as well as civil engineering applications (i.e., earthquake or seismic protection), impact absorption and vibration isolation technology in industrial engineering, and advanced prosthetics in biomedical fields. In the past, many studies have been conducted on MRDs modeling and characterization, but they have usually been focused more on the theoretical models than on the experimental issues. In this work, an overview of both of them is proposed. In particular, after an introduction to the physics of the magnetorheological effect, a short review of the main mathematical models of MRDs is proposed. Finally, in the second part of this study an overview of the main issues that occur in MRDs experimental characterization is reported and discussed.
... In Refs. [25] and [26], synthesis of isotropic compliance in E(2) and E(3) were addressed. ...
This paper addresses the passive realization of any selected planar elastic behavior with redundant elastic manipulators. The class of manipulators considered are either serial mechanisms having four compliant joints or parallel mechanisms having four springs. Sets of necessary and sufficient conditions for mechanisms in this class to passively realize an elastic behavior are presented. The conditions are interpreted in terms of mechanism geometry. Similar conditions for nonredundant cases are highly restrictive. Redundancy yields a significantly larger space of realizable elastic behaviors. Construction-based synthesis procedures for planar elastic behaviors are also developed. In each, the selection of the mechanism geometry and the selection of joint/spring stiffnesses are completely decoupled. The procedures require that the geometry of each elastic component be selected from a restricted space of acceptable candidates.
... The relation between a generalized force and its consequent generalized displacement has been studied for several purposes (e.g. [25,26] ...
Progress in MEMS technology continuously stimulates new developments in the mechanical structure of micro systems, such as, for example, the concept of so-called CSFH (conjugate surfaces flexural hinge), which makes it possible, simultaneously, to minimize the internal stresses and to increase motion range and robustness. Such a hinge may be actuated by means of a rotary comb-drive, provided that a proper set of simulations and tests are capable to assess its feasibility. In this paper, a CSFH has been analyzed with both theoretical and finite element (FEM) methods, in order to obtain the relation between voltage and generated torque. The FEM model considers also the fringe effect on the comb drive finger. Electromechanical couple–field analysis is performed by means of both direct and load transfer methods. Experimental tests have been also performed on a CSFH embedded in a MEMS prototype, which has been fabricated starting from a SOI wafer and using D–RIE (deep reactive ion etching). Results showed that CSFH performs better than linear flexure hinges in terms of larger rotations and less stress for given applied voltage.
... In Refs. [22] and [23], the synthesis of isotropic compliance in E(2) and E(3) with serial mechanisms has been addressed. In Ref. [24], conditions on mechanism geometry to achieve all compliances in E(2) were identified and synthesis procedures for the realization of an arbitrary 2 Â 2 compliance were presented. ...
This paper addresses the passive realization of any selected planar elastic behavior with a parallel or a serial manipulator. Sets of necessary and sufficient conditions for a mechanism to passively realize an elastic behavior are presented. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. The restrictions on the set of elastic behaviors that can be realized with a mechanism are described in terms of acceptable locations of realizable elastic behavior centers. Parallel–serial mechanism pairs that realize identical elastic behaviors (dual elastic mechanisms) are described. New construction-based synthesis procedures for planar elastic behaviors are developed. Using these procedures, one can select the geometry of each elastic component from a restricted space of kinematically allowable candidates. With each selection, the space is further restricted until the desired elastic behavior is achieved.
... End-point stiffness is defined as the relationship between externally applied displacements of the hand and the forces generated in response [19,20]. End-point stiffness is non-isotropic [21,22] and can be graphically represented as an ellipse [23]. Muscle patterns that modulate stiffness are studied both during dynamic [24,25] and isometric tasks [26,27]. ...
With the ageing of the workforce in the manufacturing industry, the possibility of introducing support aids such as exoskeletons to reduce the fatigue and effort of the operator has to be evaluated. An upper-limb exoskeleton with controlled impedance is expected to reduce the discomfort in the operations which require precision. Hence, arm joint stiffening is required. Real-time calculation of the exoskeleton impedance should be based on the operator’s limb impedance, evaluated through electromyographic signals. A model of the operator’s arm is necessary to identify the best control law for the exoskeleton. In this paper, preliminary considerations and a model of the elbow on which two muscles act as agonist-antagonist are presented. Numerical results are discussed, and an estimation of the performance is also proposed.
... Finally, flexure hinge compliance can cooperate with active stiffness controllers in order to optimize performances. Such collaboration can work both in serial [191][192][193][194][195][196] and parallel [197][198][199][200] MEMS-based devices. ...
This article provides an overview of the operational strategies adopted in microgrippers design. The review covers microgrippers recently proposed in Literature, some of which have been systematically presented in a companion paper, where their topological, kinematic, and structural characteristics are discussed. In the present contribution, the prevalent actuation methods and the operational aspects are discussed: the tip displacement, the tip force, the actuation voltage, and the amplification factor are the reference parameters that are adopted to compare the different types of actuation and operational strategies. In addition, the control strategies and control algorithms currently adopted are reviewed.
... The mechanical structure has an effect on its compliance response to externally applied load. The importance of such response has been recently pointed out by Rabenorosoa et al. [21], and compliance optimization, well-established in rigid-body mechanics (for example, by means of active stiffness regulation [66][67][68][69]) has been recently considered in the design of a microgripper [70]. ...
An atlas of 98 microgrippers that recently appeared in Literature is herein presented by using four different forms: (a) a restyled layout of the original mechanical structure, (b) its corresponding pseudorigid body model (PRBM), (c) its kinematic chain, and finally, (d) its related graph. Homogeneity in functional sketching (a) is assumed to be greatly helpful to understand how these grippers work and what are the most significant differences between them. Therefore, a unified and systematic set of aesthetics and proportionality criteria have been adopted. Analogously, unified criteria for obtaining pseudorigid (b), kinematic (c), and graph (d) representations have been also used, which made the atlas easy to be read and inspected. The distinction among lumped and distributed compliance has been also accepted to develop the structure of the atlas. A companion paper has been prepared to present a survey on the variety of operational strategies that are used in these microgrippers.
... Therefore, designers can assign a specific and selective compliance behavior to a compliant micromechanism to fulfill the specified requirements. This leads us to the following problem definition: "Compliance Synthesis of a compliant mechanism: the process of finding a compliant mechanism which obeys to prescribed direction-and space-dependent compliance at the tip point or at the endeffector pseudorigid link," where compliance at the tip point refers to the Euclidean group E(2) or E(3) [32], while compliance at the end effector refers to the special Euclidean group SE(3) [33]. ...
In the last decades, grippers have been employed extensively at the microscale, for example, in microbiology and in microassembly. In these fields, specifically, it is essential to improve the performance of these systems in terms of precision, actuation, and sensing of the gripping force. Recent investigations drew attention on the tip-environment interaction force, which gave rise to further studies on the tip compliance behavior. This paper reveals a new method for designing MEMS technology-based compliant microgrippers with prescribed specifications for the jaw tip compliance. This approach relies on the equivalence between a compliant mechanism and its corresponding pseudorigid-body model (PRBM), the former embedding conjugate surfaces flexure hinges (CSFHs) as flexures. Such correspondence has been assessed by means of finite element analysis (FEA) simulations and theoretical models.
In this paper, the realization of any specified planar compliance with two 3R serial elastic mechanisms is addressed. Using the concepts of dual elastic mechanisms, it is shown that the realization of a compliant behavior with 2 serial mechanisms connected in parallel is equivalent to its realization with a 6-spring fully parallel mechanism. Since the spring axes of a 6-spring parallel mechanism indicate the geometry of a dual 3R serial mechanism, a new synthesis procedure for the realization of a stiffness matrix with a 6-spring parallel mechanism is first developed. Then, this result is extended to a geometric construction-based synthesis procedure for two 3-joint serial mechanisms.
The isotropic compliance property is examined in the Special Euclidean Group SE(3) in the case of redundant manipulators. The redundancy problem is solved by means of the QR decomposition of the transposed Jacobian matrix, and the compliance property is achieved by means of active stiffness regulation. Thanks to the defined control matrices, the control system realizes the isotropy condition. The local optimization of the joint torques is discussed. In particular, the joint control torques work is minimized obtaining an analytic solution through a Lyapunov equation. The proposed approach is applied to a 7R and to a 9R serial manipulator, and verified by means of multibody dynamics simulations.
In this paper, a geometric approach to the passive realization of any planar compliance with a redundant compliant mechanism is presented. The mechanisms considered are either simple serial mechanisms consisting of five elastic joints or simple parallel mechanisms consisting of five springs. For each type of mechanism, realization conditions to achieve a given compliance are derived. The physical significance of each condition is identified and graphically interpreted. Geometry based synthesis procedures to achieve any given compliance are developed for both types of mechanisms. Since each realization condition imposes restrictions solely on the mechanism geometry, the procedures allow one to choose the geometric properties of each component (from a set of admissible options) independently from the selection of the elastic properties of each component.
This paper presents methods for the realization of 2×2 translational compliance matrices using serial mechanisms having three joints, each either revolute or prismatic and each with selectable compliance. The geometry of the mechanism and the location of the compliance frame relative to the mechanism base are each arbitrary but specified. Necessary and sufficient conditions for the realization of a given compliance with a given mechanism are obtained. We show that, for an appropriately constructed serial mechanism having at least one revolute joint, any single 2×2 compliance matrix can be realized by properly choosing the joint compliances and the mechanism configuration. For each type of three-joint combination, requirements on the redundant mechanism geometry are identified for the realization of every point planar elastic behavior at a given location, just by changing the mechanism configuration and the joint compliances.
Although tissue and cell manipulation nowadays is a common task in biomedical analysis, there are still many different ways to accomplish it, most of which are still not sufficiently general, inexpensive, accurate, efficient or effective. Several problems arise both for in vivo or in vitro analysis, such as the maximum overall size of the device and the gripper jaws (like in minimally-invasive open biopsy) or very limited manipulating capability, degrees of freedom or dexterity (like in tissues or cell-handling operations). This paper presents a new approach to tissue and cell manipulation, which employs a conceptually new conjugate surfaces flexure hinge (CSFH) silicon MEMS-based technology micro-gripper that solves most of the above-mentioned problems. The article describes all of the phases of the development, including topology conception, structural design, simulation, construction, actuation testing and in vitro observation. The latter phase deals with the assessment of the function capability, which consists of taking a series of in vitro images by optical microscopy. They offer a direct morphological comparison between the gripper and a variety of tissues.
This work studies in detail how the judicial application of compliance in parallel manipulators can produce manipulators that require significantly lower actuator effort within a range of desired operating conditions. We propose a framework that uses the Jacobian matrices of redundant parallel manipulators to consider the influence of compliance both in parallel with the actuated joints as well as the passive joints, greatly simplifying previous approaches. We also propose a simple optimization procedure to maximize the motor force reduction for desired regions of the workspace and range of external forces. We then apply the method to a Stewart-Gough platform and to a 3-URS (universal rotational and spherical joint) manipulator. Our results show that parallel manipulators with tasks that involve a preferred external force direction, as for instance, big weights in the platform, can see large reductions in actuator effort through the judicial use of compliant joints without significantly losing rigidity.
This paper presents a new concept flexure hinge for MEMS applications and reveals how to design, construct, and experimentally test. This hinge combines a curved beam, as a flexible element, and a pair of conjugate surfaces, whose contact depends on load conditions. The geometry is conceived in such a way that minimum stress conditions are maintained within the flexible beam. A comparison of the new design with the other kind of revolute and flexible joints is presented. Then, the static behavior of the hinge is analyzed by means of a theoretical approach, based on continuum mechanics, and the results are compared to those obtained by means of finite element analysis (FEA) simulation. A silicon hinge prototype is also presented and the construction process, based on single step lithography and reactive ion etching (RIE) technology, is discussed. Finally, a crucial in–SEM experiment is performed and the experimental results are interpreted through the theoretical models.
JMR Editorial – May 2011 As we move into the second decade of the 21st century, we can identify three research trends that we can expect to persist into the future. They are the analysis and synthesis of (i) spatial mechanisms and robotic systems, (ii) compliant linkage systems, and (iii) tensegrity and cable-driven systems. In each case, we find that researchers are formulating and solving polynomial systems of total degrees that dwarf those associated with major kinematics problems of the previous century. Analysis and synthesis of mechanisms and robotic systems: Early in the 2000's, E. Lee and D. Mavroidis [1] formulated the synthesis of a spatial serial chain as a generalized inverse kinematics problem, where in order to position a serial chain in a required set of task positions one computes the dimensions of the chain as well as its joint angles. About the same time general polynomial continuation algorithms such as PHCpack [2, 3] and POLSYS [4] became available. Lee and Mavroidis used PHCpack to solve 13 polynomials in 13 unknowns and obtained 36 sets of dimensions for spatial 3R chains that reach four required task positions. This system of polynomials had a total degree of 1,417,174 and took 33 days to solve on a computer workstation [5] . In 2004, H. Su and colleagues reported that a parallel version of the POLSYS code [6] obtained 42,625 solutions to the RRS design problem consisting of 11 polynomials in 11 unknowns for a total degree of 4,194,304. The computation time was 42 minutes on 128 nodes of the San Diego Supercomputer Center's Blue Horizon system. A. Perez used soma coordinates to formulate the design equations for general spatial serial chains and obtained 126 synthesis equations in 126 unknowns for a spatial 5R chain that reaches a set of 21 task positions [8, 9] (Fig. 1). This set of equations has been solved numerically to verify that they are correct, but so far a complete solution has not been achieved. Figure 1: A spatial one degree-of-freedom linkage formed from 5-5R chains.
Microrobots are used nowadays in several fields of application, specially in mini invasive surgery. However, they are rather difficult to be constructed, and the traditional micro machining tools are not adequate yet to built the smaller parts. The construction of the microrobots is even harder if more than one D.O.F. are required for the mechanism, because these systems are more complicated. This paper deals with the development of a 3 D.O.F. planar micro platform with remote system of actuation. The new approach of design and manufacturing is based on two innovative solutions: a) the adoption of the technologies used to built MEMS, Micro Electro Mechanical Systems; b) the introduction of new flexural hinge to develop compliant micro mechanisms. The new concept of flexural hinge is described in the paper, also from a theoretical point of view. Several example of possible structures are proposed and analyzed, together with their remote wire actuation systems. Finite Element Analysis (FEA) has been also adopted to analyze the system performance under small deformations. The principle of fabrication is, then, described. The process consists of a sequence of single steps which have allowed to achieved an overall maximum size down to 3-4 mm and the minimum thickness of the smaller components down to 50 μm.
A new global isotropy index (GII) is proposed to quantify the configuration independent isotropy of a robot's Jacobian or mass matrix. A new discrete global optimization algorithm is also proposed to optimize either the GII or some local measure without placing any conditions on the objective function. The algorithm is used to establish design guidelines and a globally optimal architecture for a planar haptic interface from both a kinematic and dynamic perspective and to choose the optimum geometry for a 6-DOF Stewart Platform. The algorithm demonstrates consistent effort reductons of up to six orders of magnitude over global searching with low sensitivity to initial conditions.
This paper presents a new methodology for the analysis and control of internal forces and center-of-mass (CoM) behavior, which are produced during multicontact interactions between humanoid robots and the environment. The approach leverages the virtual-linkage model that provides a physical representation of the internal and CoM resultant forces with respect to reaction forces on the supporting surfaces. A grasp/contact matrix describing the complex interactions between contact forces and CoM behavior is developed. Based on this model, a new torque-based approach for the control of internal forces is suggested and illustrated on the Asimo humanoid robot. The new controller is integrated into the framework for whole-body-prioritized multitasking, thus enabling the unified control of CoM maneuvers, operational tasks, and internal-force behavior. The grasp/contact matrix is also proposed to analyze and plan internal force and CoM control policies that comply with frictional properties of the links in contact.
In recent years, many successful robotic manipulator designs have been introduced. However, there remains the challenge of designing a manipulator that possesses the inherent safety characteristics necessary for human-centered robotics. In this paper, we present a new actuation approach that has the requisite characteristics for inherent safety while maintaining the performance expected of modern designs. By drastically reducing the effective impedance of the manipulator while maintaining high-frequency torque capability, we show that the competing design requirements of performance and safety can be successfully integrated into a single manipulation system.
Many successful robotic manipulator designs have been introduced. However, there remains the challenge of designing a manipulator that possesses the inherent safety characteristics necessary for human-centered robotics. In this paper, we present a new actuation approach that has the requisite characteristics for inherent safety while maintaining the performance expected of modern designs. By drastically reducing the effective impedance of the manipulator while maintaining high frequency torque capability, we show that the competing design requirements of performance and safety can be successfully integrated into a single manipulation system.
In this article we survey some recent developments in optimal robot design, and collect some of the differential geometric approaches into a general mathematical framework for robot design. The geometric framework permits a set of coordinate-free definitions of robot performance that can be optimized for designing both open- and closed-chain robotic mechanisms. In particular, workspace volume is precisely defined by regarding the rigid body motions as a Riemannian manifold, and various features of actuators, as well as inertial characteristics of the robot, can be captured by the suitable selection of a Riemannian metric in configuration space. The integral functional of harmonic mapping theory also provides a simple and elegant global description of dexterity.
This paper presents a simple procedure that can be used to determine the stiffness matrix of 6R serial manipulator in selected points of the work space with joint stiffness coefficients taking into account. Elastokinematical model for the robot manipulator FANUC S-420F was considered as spatial and serial kinematical chain composed of six rigid links, connected by ideal revolute joint (without clearances and deformable elements), with torsion elasticity of the joint drive system (relative torsion deformations are proportional to acted torques) taking into account. Assumed model is used for displacement analysis of the end-effector for a given applied force in quasi-static condition. The analysis results are presented as Cartesian stiffness matrix of studied manipulator.
A simple yet general method determines the stiffness matrix for parallel manipulators with serially connected legs. Link and actuator flexibilities for each leg are modeled by flexibility matrices that are additive. The effect of passive joints is implicitly included using reciprocal screws to yield a leg stiffness matrix that is generally singular. Since the legs act in parallel the leg stiffnesses are additive and yield the manipulator stiffness. The method is applicable to overconstrained, exactly constrained, and underconstrained robots in generic or singular configurations. It is illustrated using the Tricept robot containing a passive constraint leg and an overconstrained translating manipulator. Numerical results are confirmed using commercial structural analysis software.
In this paper isotropy and manipulability in RR dyads and RRP arms are analyzed and the solutions are obtained in algebraic symbolic forms. Such analysis is performed by means of two different methods: the classical approach based on the condition number and the Lie product. Although both the methods are known since decades, an accurate comparison of the two approaches has never been presented in literature. In particular, the geometrical interpretation of the Lie Product allows to appreciate some interesting differences between the two methods.
The statics and stiffness model of serial-parallel manipulators (S-PMs) formed by k parallel manipulators (PMs) connected in series is established in this paper. The S-PMs can provide features of both serial manipulators (SMs) and PMs. First, the unified formulae for solving the statics and stiffness of S-PMs are derived. Second, a k(PS + RPS + SPS) S-PM is analyzed to illustrate this model. Finally, an analytic solved example for 5(PS + RPS + SPS) S-PM is given. The established model can offer an essential theoretical basis for S-PMs. [DOI: 10.1115/1.4006190]
Variable stiffness actuators can be used in order to achieve a suitable trade-off between performance and safety in robotic devices for physical human-robot interaction. With the aim of improving the compactness and the flexibility of existing mechanical solutions, a variable stiffness actuator based on the use of flexures is investigated. The proposed concept allows the implementation of a desired stiffness profile and range. In particular, this paper reports a procedure for the synthesis of a fully compliant mechanism used as a nonlinear transmission element, together with its experimental characterization. Finally, a preliminary prototype of the overall joint is depicted.
A new plane parallel micro-manipulator is presented in this paper, together with the numerical procedure that has been used in order to optimize some kinetostatic performance indices, among which the kinematic condition number and the mechanical advantage. The approach is based on a refined simplification of the direct kinematic problem and it is applied to the pseudo-rigid body model of the original compliant mechanism, with an acceptable approximation. The method has been iterated several times to evaluate a fitness function that has been used by an Evolutionary Method of computation for the search of global optimum, namely, a Genetic Algorithm. The results will be used for refining the geometric design of the parallel micro-manipulator, which will be built by means of MEMS-Based technologies in silicon.
This paper is dedicated to the relationship between the external force applied on a point of a robot end-effector and its consequent displacement in static conditions. Both the force and the displacement are herein considered in the Euclidean space E(3). This fact represents a significant simplification of the approach, since it avoids some problems related to the absence of a natural positive definite metric on the Special Euclidean Group SE(3). On the other hand, such restriction allows the method to find closed-form solutions to a large class of problems in robot statics. The peculiar goal of this investigation consists of setting up a procedure which guarantees at least one pose at which any force applied (in E(3)) to an end-effector point is always parallel to its consequent displacement (also in E(3)). This property, which will be referred to as isotropic compliance in E(3), makes the robot tip static behavior uniform with respect to all directions, namely, isotropic, although not homogeneous, since it holds only in some poses. Achieving isotropic compliance in E(3) is a task more general than the classical problem of finding a pose with unit condition number, which does not include the case of different elements in the diagonal joint stiffness matrix. For this reason, the object of the present investigation could not be furtherer simplified to the classical kinetostatic problem in terms of the jacobian matrix alone. The paper reveals how the force–displacement parallelism can be achieved by using a method based on a simple proportional-derivative (PD) controller strategy. The method can be applied when the passive and active stiffness act, on the joints, either in parallel or in series, and the magnitude of the displacement response can be chosen by imposing appropriate values for the overall joints compliance. Results show that for the three analyzed examples, namely, the RR, RRP, and RRR manipulators, with arbitrary lengths of the links, there is, at least, one pose for which the sought property is achieved.
This paper discusses the manipulating ability of robotic mechanisms in positioning and orienting end-effectors and proposes a measure of manipulability. Some properties of this measure are obtained, the best postures of various types of manipulators are given, and a four-degree-of-freedom finger is considered from the viewpoint of the measure. The pos tures somewhat resemble those of human arms and fingers.
Variable stiffness actuators (VSAs) are currently explored as a new actuation approach to increase safety in physical human–robot interaction (pHRI) and improve dynamic performance of robots. For control purposes, accurate knowledge is needed of the varying stiffness at the robot joints, which is not directly measurable, nonlinearly depending on transmission deformation, and uncertain to be modeled. We address the online estimation of transmission stiffness in robots driven by VSAs in antagonistic or serial configuration, without the need for joint torque sensing. The two-stage approach combines (i) a residual-based estimator of the torque at the flexible transmission, and (ii) a recursive least squares stiffness estimator based on a parametric model. Further design refinements guarantee a robust behavior in the lack of velocity measures and in poor excitation conditions. The proposed stiffness estimation can be easily extended to multi-degree-of-freedom (multi-DOF) robots in a decentralized way, using only local motor and link position measurements. The method is tested through extensive simulations on the VSA-II device of the University of Pisa and on the Actuator with Adjustable Stiffness (AwAS) of IIT. Experiments on the AwAS platform validate the approach.
Industrial robots used to perform assembly applications are still a small portion of total robot sales each year. One of the main reasons is that it is difficult for conventional industrial robots to adapt to any sort of change. This paper proposes a robust control strategy to perform an assembly task of inserting a printed circuit board (PCB) into an edge connector socket using a SCARA robot. The task is very challenging because it involves compliant manipulation in which a substantial force is needed to accomplish the insertion operation and there are some dynamic constraints from the environment. Therefore, a robust control algorithm is developed and used to perform the assembly process. The dynamic model of the robotic system is developed and the dynamic parameters are identified. Experiments were performed to validate the proposed method. Experimental results show that the robust control algorithm can deal with parameter uncertainties in the dynamic model, thus achieve better performance than the model based control method. An abnormal case is also investigated to demonstrate that the robust compliant control method can deal with the abnormal situation without damaging the system and assembly parts, while pure position control method may cause damages. This strategy can also be used in other similar assembly processes with compliant applications.
Robots for use in assembly and other interactive tasks must be able to respond to both forces and velocity commands within their workspace. By considering a general six-joint robot it is shown that all such robots are limited in their ability to respond in orientation to feedback commands. It is also shown that it is simple to predict, if not to avoid, these regions of degeneracy in which the manipulator loses a degree of freedom.
The present investigation is dedicated to the study of the static balance at the tip of a planar RR robot. For this case, a configuration can be interpreted, in the static sense, as isotropic when any force applied to the robot wrist yields a small displacement which is theoretically parallel to the applied force (no matter how the force is directed on the plane). This characteristic offers many advantages and is considered as an optimal design goal. Unfortunately, the conditions to achieve such property in RR manipulators are very restrictive, and until now, only one solution is adopted, with a fixed lengths ratio. The present paper reveals how any RR planar robot can achieve isotropy at the tip by using a feedback action at the joints to gain arbitrary elastic coefficients. The new approach of design brings to less restrictive conditions than the previous ones.
This paper presents a modeling method to study the stiffness of a hybrid serial–parallel robot IWR (Intersector Welding Robot) for the assembly of ITER vacuum vessel. The stiffness matrix of the basic element in the robot is evaluated using matrix structural analysis (MSA); the stiffness of the parallel mechanism is investigated by taking account of the deformations of both hydraulic limbs and joints; the stiffness of the whole integrated robot is evaluated by employing the virtual joint method and the principle of virtual work. The obtained stiffness model of the hybrid robot is analytical and the deformation results of the robot workspace under certain external load are presented.
A theoretical study is presented on the dexterity problem of 6R manipulators, particularly, the manipulator's service angle around a reachable point in space. The first part conceptualizes the ideas of service region, free service region and polarities of robots, and shows that the entire service angle can be categorized into a number of free service regions. The remainder deals with the investigation of basic properties of free service regions. The relationship between free service regions and service angle is subsequently formulated into a set of theorems and criteria. Specific examples are given for illustration.
In this article we survey some recent developments in optimal robot design, and collect some of the differential geometric approaches into a general mathematical framework for robot design. The geometric framework permits a set of coordinate-free definitions of robot performance that can be optimized for designing both open- and closed-chain robotic mechanisms. In particular, workspace volume is precisely defined by regarding the rigid body motions as a Riemannian manifold, and various features of actuators, as well as inertial characteristics of the robot, can be captured by the suitable selection of a Riemannian metric in configuration space. The integral functional of harmonic mapping theory also provides a simple and elegant global description of dexterity.
Kinematic and control issues are discussed in the context of an articulated, multifinger mechanical hand. Hand designs with particular mobility properties are illustrated, and a definition of accuracy points within manipulator workspace is given. Optimization of tlte physical dimensions of the Stanford-JPL hand is described. Several architectures for position and force control of this multiloop mechanism are described, including a way of dealing with the internal forces inherent in such systems. Preliminary results are shown for the joint torque subsystem used in the hand controller.
The conditioning index of a serial robotic manipulator is de fined in this article in terms of the reciprocal of its minimum condition number. The condition number of a manipulator is defined, in turn, as that of its Jacobian matrix. Moreover, in defining the Jacobian condition number, a quadratic norm of the Jacobian matrix is needed. However, this norm, or for that matter any other norm, brings about dimensional inho mogeneities. It is shown here that by properly defining the said norm based on a weighting positive definite matrix, the dimensional inhomogeneity is resolved. Manipulators with a conditioning index of 100% are termed isotropic, a six-axis isotropic manipulator being introduced. This manipulator has all its angles between neighboring revolute axes at 90° and all its distances between neighboring axes identical; more over, these distances are identical to the offsets of those axes. The kinematic conditioning of wrist-partitioned manipulators is given due attention, and illustrated with some examples of industrial robots of this type.
The design of redundant isotropic architectures for robotic nia nipulators is the subject of this article. A manipulator is said to have a redundant isotropic architecture if (1) its number of controlled axes is greater than the dimension of its task space. and (2) it is possible for the manipulator to attain configura tions at which all the singular values of its Jacobian matrix are identical and nonzero. The concept of isotropy, which has already been applied to the design of nonredundant manip ulators, is applied to the design of redundant ones. General geometric conditions on the manipulator parameters and on its configuration variables under which isotropy is attained are derived.
Previous work on posture optimization for robots has examined the condition number as a measure of kinematic dexterity. When the condition number equals an optimal value of one, the robot is described as isotropic. Isotropic configurations have a number of advantages, including good servo accuracy, noise rejection, and singularity avoidance. This article introduces a definition for spatial isotropy of a robot, which is combined isotropy for both positioning and orienting the end effector. Generally iso tropy may be used either as a robotic design criterion or as a posture optimization function for redundant manipu lators. This work demonstrates design techniques using positional, orientational, or spatial isotropy and presents some algorithms for locating isotropic designs without explicit evaluation of singular values. Several representa tive robot designs illustrate these concepts for both nonre dundant and redundant manipulators.
In this paper, we have proposed a number of measures for the quantification of dexterity of manipulators. The use of such measures is especially important for kinematically redundant manipulators since they can satisfy secondary cri teria in addition to satisfying a specification of end-effector motion. We will compare several measures for the problems offinding an optimal configuration for a given end-effector position, finding an optimal workpoint, and designing the op timal link lengths of an arm.
A NEW THEORY AND A RESULTING ALGORITHM FOR TRACING THE BOUNDING SURFACES OF MECHANICAL MANIPULATOR WORKSPACES IS PRESENTED. THE NATURES OF THE NUMEROUS SINGULAR CONFIGURATIONS ANDMEANS OF ACCOMMODATING THEM WITHIN THE ALGORITHM ARE ALSO STUDIED. IN ORDER TO SORT SURFACES OF INTEREST FROM THE LARGENUMBER OF POSSIBLE SOLUTIONS, A NUMERICALLY IMPLEMENTABLE LABELLING TECHNIQUE IS ALSO PRESENTED. THE ALGORITHM IS APPLICABLE TO ALL PRACTICABLE MANIPULATOR CONFIGURATIONS WITH THREE, OR MORE, DEGREES OF FREEDOM.
In this paper, a novel performance index for the kinematic optimization of robotic manipulators is presented. The index is based on the condition number of the Jacobian matrix of the manipulator, which is known to be a measure of the amplification of the errors due to the kinematic and static transformations between the joint and Cartesian spaces. Moreover, the index proposed here, termed global conditioning index (CGI), is meant to assess the distribution of the aforementioned condition number over the whole workspace. Furthermore, the concept of a global index is applicable to other local kinematic or dynamic indices. The index introduced here is applied to a simple serial two-link manipulator, to a spherical three-degree-of-freedom serial wrist, and to three-degree-of-freedom parallel planar and spherical manipulators. Results of the optimization of these manipulators, based on the GCI, are included.
This investigation deals with singularity analysis of parallel manipulators and their in-stantaneous behavior while in or close to a singular configuration. The method presented utilizes line geometry tools and screw theory to describe a manipulator in a given posi-tion. Then, this description is used to obtain the closest linear complex, presented by its screw coordinates, to the set of governing lines of the manipulator. The linear complex axis and pitch provide additional information and a better physical understanding of the type of singularity and the motion the manipulator tends to perform in a singular point and in its neighborhood. Examples of Hunt's, Fichter's and 3-UPU singularities, along with a few selected examples taken from Merlet's work [1], are presented and analyzed using this method.
The variable stiffness actuation (VSA) technology
has been recently developed and applied in robotic arms.
Mechanism robustness, high peak torque and velocity, and
stiffness adjustment flexibility are key benefits of VSA joints.
However, the achievable Cartesian stiffness by uncoupled VSA
joints is limited. Therefore we suggest and analyze the use of
an active impedance controller in combination with the passive
joints to further increase the stiffness range. An algorithm to
optimize the passive and active Cartesian stiffness is proposed to
achieve a desired Cartesian stiffness as precise as possible. The
algorithm was implemented and tested on the VSA robot DLR
Hand Arm System. Experimental results and measurements of
the active/passive impedance algorithm are shown.
Variable stiffness actuators are a particular class of actuators that is characterized by the property that the apparent output stiffness can be changed independent of the output position. To achieve this, variable stiffness actuators consist of a number of elastic elements and a number of actuated degrees of freedom, which determine how the elastic elements are perceived at the actuator output. Changing the apparent output stiffness is useful for a broad range of applications, which explains the increasing research interest in this class of actuators. In this paper, a generic, port-based model for variable stiffness actuators is presented, with which a wide variety of designs can be modeled and analyzed. From the analysis of the model, it is possible to derive kinematic properties that variable stiffness actuator designs should satisfy in order to be energy efficient. More specifically, the kinematics should be such that the apparent output stiffness can be varied without changing the potential energy that is stored in the internal elastic elements. A concept design of an energy-efficient variable stiffness actuator is presented and implemented. Simulations of the model and experiments on the realized prototype validate the design principle.
This paper presents a general and systematic approach to formulate the dimensionally homogeneous Jacobian, which is an important issue for the dexterity evaluation and dimensional synthesis of
f
-degrees-of-freedom (DOF) (
f
≤ 6) parallel manipulators having mixed rotational and translational movement capabilities. By the utilization of
f
independent coordinates to describe the specified motion types of the platform, the
f
×
f
dimensionally homogeneous Jacobian is derived directly from the generalized Jacobian, provided that the manipulator has only one type of actuator. The condition number of the new Jacobian is then employed to evaluate the dexterity of two typical 3-DOF parallel manipulators as an illustration of the effectiveness of this approach.
The paper presents a new structural synthesis approach of fully-isotropic translational parallel robotic manipulators (TPMs) based on the theory of linear transformations. A TPM is a 3-DOF (degree of freedom) parallel mechanism whose output link, called platform, can achieve three independent orthogonal translational motions with respect to the fixed base. The manipulators presented in this paper have three legs connecting the moving platform and the base (fixed platform). Only one kinematic pair per leg is actuated by a linear motor situated on the fixed base. A one-to-one correspondence exists between the actuated joint space and the operational space of the moving platform. The Jacobian matrix of fully-isotropic TPMs presented in this paper is the identity 3×3 diagonal matrix throughout the entire workspace. The synthesis method proposed in this paper allows us to obtain all structural solutions of fully-isotropic TPMs in a systematic manner. Overconstrained/isostatic solutions with elementary/complex and identical/different legs are obtained. Fully-isotropic TPMs have the advantage of simple command and important energy-saving due to the fact that, for a unidirectional translation, only one motor works as in a serial translational manipulator.
The article presents a brief tutorial on classical line geometry and investigates new aspects of line geometry which arise in connection with a computational treatment. These mainly concern approximation and interpolation problems in the set of lines or line segments in Euclidean three-space. In particular, we study the approximation of data lines by, in a certain sense, ‘linear’ families of lines. These sets are, for instance linear complexes and linear congruences. An application is the reconstruction of helical surfaces or surfaces of revolution from scattered data points. This is based on the fact that the normals of these surfaces lie in linear complexes; in particular, normals of surfaces of revolution intersect the axis of revolution.Approximation with linear complexes or congruences is also useful in detecting singular positions of serial or parallel robots. These are positions where the robot should be a rigid system but possesses an undesirable and unexpected instantaneous self motion.
In this article we develop a mathematical theory for optimizing the kinematic dexterity of robotic mechanisms and obtain a collection of analytical tools for robot design. The performance criteria we consider are workspace volume and dexterity; by the latter we mean the ability to move and apply forces in arbitrary directions as easily as possible. Clearly, dexterity and workspace volume are intrinsic to a mechanism, so that any mathematical formulation of these properties must necessarily be independent of the particular coordinate representation of the kinematics.
By regarding the forward kinematics of a mechanism as defining a mapping between Riemannian manifolds, we apply the coordinate-free language of differential geometry to define natural measures of kinematic dexterity and workspace volume. This approach takes into account the geometric and topolog ical structures of the joint and workspaces. We show that the functional associated with harmonic mapping theory provides a natural measure of the kinematic dexterity of a mechan ism. Optimal designs among the basic classes of mechanisms are determined as extrema of this measure. We also examine the qualitative connections between kinematic dexterity and workspace volume.
In this paper, the concepts of connectivity, degrees of control, and redundancy are revisited from a pure topological viewpoint and then applied to robotics. The redundancy matrix is defined to provide designers with a useful support in the first conceptual phase of the project of a new manipulator. An algorithm for building the connectivity and the redundancy matrices for a large class of manipulators is derived and implemented in an algebraic manipulation programming language. Based on some results borrowed from graph theory, the procedure can be used to study open-loop, closed-loop, and hybrid kinematic chains. In particular, it is shown how the biconnected components of the graph corresponding to the manipulator under analysis have to be detected for a correct computation of connectivity and redundancy. Furthermore, the study of the connectivity and of the degrees of control led to the development of a full mobility test that automatically detects the type of mobility of any given robot: total, partial, or fractionated. One of the presented sample cases offers the opportunity to discover some differences between the connectivity matrix obtained by means of the new algorithm and that presented, on the same kinematic chain, in a previous one.
A volumetric method of kinematic analysis of a manipulator which can be used in addition to the conventional trajectory method is presented. An ideal manipulator, the influence of limitations on the angles of rotation of the manipulator, and a manipulator with limitations in all joints are discussed.
In the field of service robotics, whole arm contact with an unstructured environment or human beings becomes a major issue. Therefore soft robots, which mean robots with passively (or mechanically) compliant joints, become more and more important. In this work we analyze what Cartesian stiffness at the tool center point one can achieve with a passively compliant, redundant robot with variable joint stiffness. We restrict this work to the special case of uncoupled joint stiffness only, as coupling of joint stiffness seems to be mechanically difficult to realize. Finally we discuss a Cartesian controller, which incorporates the compliance of the joints and ensures the correct stiffness behavior also for high displacements from the desired position.
The authors investigate dexterity measures of a manipulator based
on its Jacobian matrix. The goal is to derive dexterity measures which
can be used for both design and control of a manipulator. Generally, a
dexterity measure must be independent of the scale of a manipulator for
design, and must be expressed analytically so that it can be used for
real-time control. Every dexterity measure must bear a physical meaning.
The measure of manipulability has an analytical expression, but it
depends on the scale of a manipulator. On the other hand, the condition
number is independent of the scale, but cannot be expressed
analytically. These two main problems (scale dependency and analytical
expression) of previous dexterity measures derived from the Jacobian
matrix are solved and applied in design and control of manipulators. In
addition, a dexterity measure called the measure of isotropy is
introduced
In this paper, nonlinear stiffness of contact for soft fingers, commonly used in robotic grasping and manipulation, under a normal load is studied. Building upon previous research results of soft-finger contact expressed in the power-law equation, the equation for the nonlinear stiffness of soft contact was derived. This new theory relates the approach displacement (or the vertical depression) of soft fingertips with respect to the normal force applied. The nonlinear contact stiffness is found to be the product of an exponent and the ratio of the normal force versus approach displacement. Stiffness relationship of Hertzian contact for linear elastic materials is shown to be a special case of the general theory presented in this paper. Experimental results are used to validate the theoretical analysis. In addition, potential applications to fixturing are discussed.
Realization of an Arbitrary Planar Stiffness With a Simple Symmetric Parallel Mechanism
Huang, S., and Schimmels, J., 2011, "Realization of an Arbitrary Planar Stiffness With a Simple Symmetric Parallel Mechanism," ASME J. Mech. Rob.,
3(4), p. 041006.
Stiffness Evaluation of Machines and Robots: Minimum Collinear Stiffness Value Approach
Portman, V., 2011, "Stiffness Evaluation of Machines and Robots: Minimum
Collinear Stiffness Value Approach," ASME J. Mech. Rob., 3(1), p. 011015.