# Mechanism and Machine Theory

Published by Elsevier

Online ISSN: 0094-114X

Published by Elsevier

Online ISSN: 0094-114X

Publications

Conference Paper

The approach is based upon the online planning of suitable alternative instantaneous motions (velocities). Planned alternative velocities are used to replace impracticable desired velocity specifications. Joint rate truncation and optimization subject to motion feasibility constraints are used to plan the alternative motion. The motion feasibility constraints are determined by screw quantities reciprocal to the nontruncated joint axes. A method is presented for resolving the reciprocal screw quantities required to enforce alternative motion feasibility. The method is suitable for manipulators having a least one pair of intersecting revolute axes

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Conference Paper

Humanoid robots and robotic manipulators with good dexterity are promising to enhance the factory productivity in next generation. Dexterity of robotic manipulators can be achieved by equipping an anthropomorphic robot hand with multiple fingers. Additionally, in order to manipulate various tools that humans are using in daily life, the size and the exerting force of the robot hand should be similar to that humans are. In this paper, we proposed a human-sized multi-fingered robot hand with detachable mechanism at the wrist. The robot hand can be split at the wrist into the hand part and the actuator part. The fingers are driven by wires and are controlled by actuators embedded in the arm part. The driving force from the arm part is transmitted to the hand part by gear mechanism at the wrist. The developed robot hand has the size of 200[mm](length) Ã 78[mm](width) Ã 24.6[mm](thickness) and can exert 10[N] at the fingertip. The performance of the developed robot hand was shown by a motion control experiment.

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Conference Paper

Most robust control methods of robot manipulators guarantee small
tracking errors by applying sufficiently high feedback gains. Infinite
gains are required for zero tracking errors. However, in practice,
feedback gains could be severely limited by hardware factors. Robust
control schemes using low feedback gains are desirable. In this paper,
we derive a globally asymptotically stable robust control scheme by
combining integral control with a robust saturation control law. The
proposed robust control method takes advantage of both saturation
control and integral control techniques, while the disadvantages
attributed to them are remedied by each other. Globally asymptotic
stability of an n-link robot system with parametric model uncertainties
is achieved. As an illustration, the proposed control scheme is applied
to a two degrees-of-freedom direct drive robot arm. Simulations were
conducted, and the results are in accordance with the theoretical
analysis

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Conference Paper

The general mathematical model of multiple rigid robot
manipulators performing cooperative work on a single dynamical object of
which the motion is constrained by a dynamical environment is presented.
The coordinated robots have to simultaneously move the object along a
predetermined known trajectory on the constraint environment, exert a
prespecified contact force on the environment, and keep the value of the
internal force between a certain minimum and maximum. The manipulator
dynamics, the object dynamics and the environment dynamics are taken
into consideration, together with the contact conditions between robots
and object and between object and environment

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Conference Paper

Two fast computational schemes for robot inverse dynamics are presented. One scheme is designed to implement the inverse dynamics computation for a robot in real-time on a microcomputer with only one processor. In this scheme, two efficient algorithms that are computationally the fastest of all the existing single-processor-based algorithms for the robot inverse dynamics computation are proposed. The scheme is designed to implement in parallel the real-time inverse dynamics computation for a robot on a microcomputer with three processors. The proposed algorithms have been verified by computing the inverse dynamics of a PUMA 560 robot arm with six degrees-of-freedom

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Conference Paper

The Navy is developing a deep-ocean work system comprised of manipulators and a variety of hydraulic tools integrated to accomplish meaningful work tasks to ocean depths of 20,000 ft. The system can be readily adapted to the manned submersibles ALVIN, SEACLIFF, and TURTLE, and the robot vehicles CURV III and RUWS, to extend their work capability. In addition, it can be positioned and controlled by divers or operated by itself from a surface support ship. The system was designed to perform a complete work operation on the sea floor without the necessity of resurfacing for tool interchange. Potential tasks include recovery, construction, installation, and repair operations. Low-light level TV cameras, with quartz-iodide flood lights, augment the vehicle operator's vision for tool exchange and work operations.

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Conference Paper

Presents a general solution for the direct kinematics of planar
three-degree-of-freedom parallel manipulators. It has been shown
elsewhere, using geometric considerations, that this problem can lead to
a maximum of six real solutions. The formulation developed leads to a
polynomial of the sixth order which is hence minimal. This is
illustrated with an example, taken from the literature, for which six
real solutions have been found. Moreover, for a special geometry in
which the three joints on the platform and on the base are respectively
aligned, it is shown that the solution can be cascaded in two steps
involving the solution of a cubic and a quadratic respectively. This
particular class of planar parallel manipulators can therefore be solved
in closed-form and no more than four real solutions have been found in
this case. Examples of this class of manipulators are also solved

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Article

This paper presents an experimental and analytical study of nonlinear dynamics of air bearing slider in modern hard disk recording system. Proximity recording sliders used for commercial hard disk drive were deployed for the experimental investigation. Flying height oscillation signal of the sliders in various proximity regimes (nano-meter level) were measured by using ultra-precision laser doppler vibrometer (LDV), and processed by using Matlab for time–frequency analysis and phase plot analysis. From the experimental results, it was found that two kinds of nonlinear oscillations exist in the system: the slider–disk contact-induced nonlinearity and the air bearing inherent nonlinearity. Primary resonance, superharmonic resonance and sub-harmonic resonance due to the nonlinearity were observed. A numerical–analytical model incorporating the nonlinear features of both slider air bearing oscillation and slider contact vibration was developed to quantitatively estimate spectral signatures. Direct numerical simulations were also carried out to simplified model to obtain phase plots. The analytical and numerical results agree with the experimental results well. It was shown that both the contact vibration and air bearing oscillation render the system to exhibit complex nonlinear features. Particularly, phase plots can be used to identify the slider–disk contact vibration and air bearing nonlinear oscillation, the former is characterized by “sharp corner” when the non-contact phase transferring to contact phase, and latter is characterized by “smooth corner” due to stiffness–softening feature of air bearing.

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Article

This paper deals with some chariots belonging to the Egyptian Pharaoh Tut Ankh Amun, used in 1337 B.C. and discovered in his tomb in the Valley of Kings in 1922. One of the chariots was restored by Nadia Lokma and theoretically studied by Dr. Nasry Iskander at the Egyptian Museum in Cairo. Some mechanical aspects of the structure of the wheels, the spokes, the materials chosen for the sleeve bearings, the use of animal grease for lubrication and the design of the chariot as a whole are extraordinary. In fact, they are very similar to the technical and scientific principles used in machine mechanics with some of the modern concepts of today’s applications.

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Article

Presented in this paper is on the nonlinear dynamics of a planetary gear system with multiple clearances taken into account. A lateral–torsional coupled model is established with multiple backlashes, time-varying mesh stiffness, error excitation and sun-gear shaft compliance considered. The solutions are determined by using harmonic balance method from the equations in matrix form. The theoretical results from HBM are verified by using the numerical integration. Finally, effects of parameters are discussed.

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Article

An algorithm to exhaustively enumerate and structurally classify planar simple-jointed kinematic chains using the hierarchical representation of Fang and Freudenstein is proposed in which all isomorphic chains are automatically eliminated in the enumeration procedure such that isomorphism testing on the final set of chains is eliminated. An efficient rule-based technique for eliminating degenerate kinematic chains is also proposed. This efficient scheme allows for the exhaustive enumeration of complicated cases that have received little or no attention in the past due to the difficult and time-consuming aspect of testing the kinematic chains for isomorphisms. For verification, the algorithm is first applied to enumerate the single degree-of-freedom 6-, 8-, and 10-bar cases, then to the 12-bar case (for which the results verify or contradict those reported in three previous papers), and finally to the previously intractable 14-bar case.

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Article

In this paper the work on the Theory of Machines by Galilei is reviewed and interpreted. The small treatise Le Mecaniche can be considered of fundamental significance in the History of Mechanical Engineering since it was written for a first academic course on TMM, and it used modern concepts.

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Article

Shifts in a dual-clutch transmission (DCT) are realized by torque transfer from one clutch to another without traction interruption due to the controlled slippage of the clutches. The timing of engagement and disengagement of the two clutches is critical for achieving a smooth shift without engine flare and clutch tie-up. This paper presents an analytical model for the simulation, analysis and control of shift dynamics for DCT vehicles. A dynamic model and the control logic for the integrated vehicle have been developed using Matlab/Simulink as the simulation platform. The model has been used to study the variation in output torque in response to different clutch pressure profiles during shifts. Optimized clutch pressure profiles have been created for the best possible shift quality based on model simulation. As a numerical example, the model is used for a DCT vehicle to simulate the wide-open throttle performance. Vehicle launch and shift process are both simulated to assess transmission shift quality and validate the effectiveness of the shift control.

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Article

The paper presents a method for the complete shaking force and shaking moment balancing of 17 types of eight-bar linkages only with revolute pairs due to both linear and rotary inertia, but external loads. The method is a combination of mass redistribution and addition of two kinds of the interia counterweights, which are the geared inertia counterweight and the planetary-gear-train-inertia counterweight. The design equations for full force and moment balancing of 17 types of the eight-bar linkages are given.РефератPaзpaбoтaн мeтoд иypaвнeния ддя пoлнoгo ypaвнoвeшивaния cил и пap инepции цeмнaдцaти видoв плocкич вocъмизвeнняч мeчaнизмoв c вpaшaтeлънями пapaми. Meтoд ocнoвaн нa пpимeиeнни пoтивoвecoв нa зyбyaтяч кoлecaч, вpaшaющичcя вoкpyг нeпoдвижныч oceй, a тaкжe coвepшaюшич плaнeтapoe днижeниe.

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Article

This biography highlights the historical importance of Ferdinand Redtenbacher for the evolution of mechanical engineering to technical science in the 19th century. The presentation substantially follows
[6] and [15] with regard to personal biographical details by Ferdinand Redtenbacher himself,
[1],
[22],
[23],
[24],
[25],
[26],
[27],
[28],
[29],
[30],
[31],
[32] and [33], essays by contemporary witnesses in
[7],
[9],
[10],
[11],
[12] and [34] (but not so much [2], see [40]) as well as historical appraisals in
[13],
[14],
[37] and [38]. It starts with a description of his life covering his childhood and early teens in his home in Upper Austria, through the culmination of his professional career as a professor and the director of the Polytechnic school in Karlsruhe, Germany (today the University of Karlsruhe). Of particular interest is the question of which external circumstances and characters helped to establish the path of Redtenbacher’s lifework and how his influence pushed the German manufacturing engineering in the 20th century and even today. Finally this paper explores Redtenbacher’s contributions to mechanism and machine science by means of his construction of kinematic models for teaching.

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Article

This special issue on computer-aided design of mechanisms has the objective of representing the state-of-the-art in computer-assisted mechanism analysis and synthesis. The events of the past 25 years are reviewed in this article. The brief look at today and the potential future of this fast-growing area are meant to set the stage for this special issue of Mechanism and Machine Theory.

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Article

This paper introduces a novel configuration space method for analyzing the relative mobility of a body B, in frictionless quasi-static contact with rigid stationary bodies A1, …, Ad. We study the 1st order properties of Bs free motions and relate them to the reciprocal/repelling screws of Screw Theory. This analysis forms the basis for a 1st order mobility theory. We introduce a coordinate invariant mobility index that measures the effective 1st order mobility of B in an equilibrium grasp. This index is shown to be solely a function of the number of the contact points. Examples show that the 1st order mobility theory (and hence Screw Theory) cannot adequately differentiate between different equilibrium grasps involving the same number of fingers. This motivates the development of a 2nd order theory in the companion paper. The 2nd order analysis is facilitated by the configuration space approach developed herein.

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Article

During the creation of a modern machine system, the designer must generally develop a mathematical model to investigate the levels of vibrational activity, dynamic stresses, bearing loads and often the acoustic radiation associated with the system. Since all of these phenomena may be represented by field theories whose governing equations of motion may be stated as either differential, integral or integro-differential equations, they are all amenable to solution by the single most powerful computational tool available to the analyst: the finite element method. Mechanism design methodologies based on this versatile technique are reviewed herein, their different characteristics are highlighted and future trends indicated.ZusammenfassungBei der Entwicklung moderner Maschinensysteme muβ der Konstrukteur im allgemeinen ein mathematisches Modell aufstellen, um den Grad der Schwingungsaktivität, der dynamischen Beanspruchungen, der Lagerbelastungen und oft auch der akustischen Ausstrahlung des Maschinensystems untersuchen zu können. Da solche Erscheinungen durch Theorien repräsentiert werden, deren maβgebende Bewegungsgleichungen entweder als Differential-Integral- oder Integro-Differentialgleichungen darstellbar sind, können sie alle mit einem einzigen sehr wirkungsvollen Computer-Mittel, das jedem für diese Analyse zugänglich ist, einer Lösung zugeführt werden: mit der Finite-Element-Methode. Es werden die Methodologien für Mechanismenkonstruktionen, die auf dieser vielseitigen Technik basieren, besprochen, ihr unterschiedlicher Charakter beleuchtet und zukünftige Trends angegeben.

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Article

This paper presents a volumetric error analysis and an architecture optimization method for accuracy of parallel manipulators. A comprehensive volumetric kinematic error model that relates all kinematic error sources in the manipulator’s architecture to the pose errors of the end-effector is derived for HexaSlide (US) type parallel manipulators. The error model results in the total error transformation matrix from which three error amplification factors are derived and used as design criteria for accuracy in the optimum design formulation with constraints on workspace and design variable limits. Then, design optimization for accuracy has been performed by using a nonlinear optimization technique. Optimization results have been validated by Monte Carlo statistical simulation technique.

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Article

Using a configuration space approach, this paper develops a 2nd order mobility theory for a body B, in frictionless quasi-static contact with rigid stationary bodies A1,…,Ad. This analysis ultimately leads to a coordinate invariant 2nd order mobility index, an integer that captures the inherent mobility of B in an equilibrium grasp. The 2nd order index differentiates between grasps which are deemed equivalent by 1st order, or instantaneous, theories, but are physically different. We further show that 2nd order effects can be used to lower the effective mobility of an equilibrium grasp, and hence can be used to prove new lower bounds on the number of contacting bodies needed to immobilize an object.

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Article

This paper presents a control strategy for a two-link manipulator with revolute joints (2R) with an unactuated second joint, wherein the motion of the system is confined to a horizontal plane. The model takes into account the frictional forces present in the system. The control objective is to move the end-effector from a given position to a target point. The methodology involves two stages. In the first stage a finite-time controller is used to move the passive link to its desired position. In the second stage, the first link is moved to its desired position keeping the second link at rest, using friction as a “brake” and subject to the constraint that the cross-coupling torque acting on the second joint does not exceed the static friction.

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Article

This paper addresses the problem of singularity-free path planning for the six-degree-of-freedom parallel manipulator known as the Stewart platform manipulator. Unlike serial manipulators, the Stewart platform possesses singular configurations within the workspace where the manipulator is uncontrollable. An algorithm has been developed to construct continuous paths within the workspace of the manipulator by avoiding singularities and ill-conditioning. Given two end-poses of the manipulator, the algorithm finds out safe (well-conditioned) via points and plans a continuous path from the initial pose to the final one. When the two end-poses belong to different branches and no singularity-free path is possible, the algorithm indicates the impossibility of a valid path. A numerical example has also been presented as illustration of the path planning strategy.

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Article

A model is presented which enables the simulation of the three-dimensional dynamic behaviour of planetary/epicyclic spur and helical gears. Deformable ring-gears are introduced by using either beam elements for simple structures, or 3D brick elements for complex geometries. Based on a modal condensation technique, internal gear elements can be defined by connecting the ring-gear sub-structure and a planet lumped parameter model via elastic foundations which account for tooth contacts. Discrete mesh stiffnesses and equivalent normal deviations are introduced along the contact lines, and their values are re-calculated as the mating flank positions vary with time. Planetary/epicyclic gear models are completed by assembling lumped parameter sun-gear/planet elements along with shaft elements, lumped stiffnesses, masses and inertias. The corresponding equations of motion are solved by combining a time-step integration scheme and a contact algorithm for all simultaneous meshes. Several quasi-static and dynamic results are given which illustrate the potential of the proposed hybrid model and the interest of taking into account ring-gear deflections.

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Article

This paper proposes a general formulation of the kinetostatic model of articulated wheeled rovers that move on rough terrains. Differential kinematic model is used to control the generalized trajectory of the robot, composed of position and posture parameters. These posture parameters have been optimized in order to provide high stability and traction performance, during motion on irregular ground surface. Numerical simulation and experimental results, carried out on a hybrid wheeled–legged robot, show the validity of the approach presented in this paper.

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Article

In this paper, a novel approach to carry out the design of a three degrees of freedom (3DOF) actuated mechanisms for humanoid robots joints is presented. Instead of common serial mechanism, a more robust parallel mechanism was developed. This kind of structure gives the terminal body the ability to move within a cone from the nominal position and permits unlimited rotation about the cone pointing axis. Kinematic analysis are presented in this paper. A biped robot ROBIAN with parallel hip and ankle mechanisms was developed and experimental tests were carried out to evaluate the performances of the adopted structure.

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Article

In this paper, we constrain a planar serial chain formed by three revolute joints, so that it becomes a one degree-of-freedom six-bar linkage. Our focus is on the various ways that two RR chains can be attached to constrain the links of the 3R chain, and ensure that the end-effector passes through a set of five specified task positions.This synthesis process yields designs for the Watt I and Stephenson I, II, and III six-bar linkages. This approach does not apply to the Watt II because its floating link is not connected to the ground frame by a 3R chain. We demonstrate the synthesis process with the design of a six-bar steering linkage intended for use on a gravity racer.

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Article

This paper analyses the workspace of the three-revolute orthogonal manipulators that have at least one of their DH parameters equal to zero. These manipulators are classified into different groups with similar kinematic properties. The classification criteria are based on the topology of the workspace. Each group is evaluated according to interesting kinematic properties such as the size of the workspace subregion reachable with four inverse kinematic solutions, the existence and the size of voids, and the size of the regions of feasible paths in the workspace.

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Article

Manipulator design can be conveniently expressed as a function of workspace requirements, since a fundamental feature of manipulators is recognized in workspace capabilities. In this paper a suitable formulation for the workspace has been used for the manipulator design, which has been formulated as multi-objective optimization problem by using the workspace volume and robot dimensions as objective functions, and given workspace limits as constraints. Additional constraints have been included to obtain manipulator sizes within practical values. The optimum design has been successfully tested by numerical examples, which have also proved the efficiency of using an algebraic formulation for the workspace of 3R manipulators.

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Article

This paper describes how the forward and inverse position, velocity and acceleration kinematics of a spherical 4R wrist—with coupled second and third joint axes—can be transformed efficiently into the kinematics of a well-known equivalent spherical 3R wrist. The transformation relies on one variable parameter α (which is very easy to calculate), and on a fixed design parameter β. Industrial implementations exist for some specific values of β.

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Article

Using a novel geometric factorization of the singularity set, this paper enumerates all non-generic 3R manipulator geometries. These geometries divide the space of all 3R manipulator geometries into disjoint sets which have similar topological properties. Their enumeration serves as a classification scheme for all 3R manipulators. Some preliminary conjectures on 3R manipulators which can or can not change pose without passing through a singular configuration are presented as one application of these results.

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Article

Some of the results presented in [J. W. Burdick, Mechanism and Machine Theory30, 71–89 (1995)] are discussed here, namely: 1. the remark pertaining to the relationship between non-genericity and solvability; 2. the conjecture about non-singular pose flipping, non-genericity, an extra-branch singularities; 3. the list of non-generic 3R manipulator geometries.

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Article

A novel 3SPU + UPR parallel manipulator with three rotations and one translation is proposed. Its kinematics is analyzed systematically, and its workspace and active/constrained forces are solved. First, its simulation mechanism is created, and the formulae for solving the inverse/forward displacement kinematics are derived. Second, the formulae for solving inverse/forward velocity, active forces and constrained forces are derived. Third, the formulae for solving inverse/forward acceleration are derived and a workspace is constructed. Finally, the analytic results are verified by its simulation mechanism.

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Article

Parallel robots with Schoenflies motions (also called 3T1R parallel robots) are increasingly being used in applications where precision is of great importance. Clearly, methods for evaluating the accuracy of these robots are therefore needed. The accuracy of well designed, manufactured, and calibrated parallel robots depends mostly on the input errors (sensor and control errors). Dexterity and other similar performance indices have often been used to evaluate indirectly the influence of input errors. However, industry needs a precise knowledge of the maximum orientation and position output errors at a given nominal configuration. An interval analysis method that can be adapted for this purpose has been proposed in the literature, but gives no kinematic insight into the problem of optimal design. In this paper, a simpler method is proposed based on a detailed error analysis of 3T1R fully-parallel robots that brings valuable understanding of the problem of error amplification.

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Article

In this paper, a novel 4-DOF decoupled parallel manipulator with Schoenflies motions, called the Pantopteron-4, is presented. This manipulator is able to perform the same movements as the Isoglide4 or the Quadrupteron, but, due to its architecture which is made of three pantograph linkages, an amplification of the movements between the actuators and the platform displacements is achieved. Therefore, having the same actuators for both robots, the Pantopteron-4 displaces (theoretically) many-times faster than the Isoglide4 or the Quadrupteron, depending on the magnification factor of the pantograph linkages. Thus, this mechanism is foreseen to be used in applications where the velocities and accelerations have to be high, as in pick-and-place. First, the kinematics of the Pantopteron-4 is presented. Then, its workspace is analyzed. Finally, a prototype of the mechanism is shown and conclusions are given.

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Article

A new method for smooth trajectory planning of robot manipulators is described in this paper. In order to ensure that the resulting trajectory is smooth enough, an objective function containing a term proportional to the integral of the squared jerk (defined as the derivative of the acceleration) along the trajectory is considered. Moreover, a second term, proportional to the total execution time, is added to the expression of the objective function. In this way it is not necessary to define the total execution time before running the algorithm. Fifth-order B-splines are then used to compose the overall trajectory. With respect to other trajectory optimization techniques, the proposed method enables one to set kinematic constraints on the robot motion, expressed as upper bounds on the absolute values of velocity, acceleration and jerk. The algorithm has been tested in simulation yielding good results, which have also been compared with those provided by another important trajectory planning technique.

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Article

The paper presents a new stiffness modeling method for overconstrained parallel manipulators with flexible links and compliant actuating joints. It is based on a multidimensional lumped-parameter model that replaces the link flexibility by localized 6-dof virtual springs that describe both translational/rotational compliance and the coupling between them. In contrast to other works, the method involves a FEA-based link stiffness evaluation and employs a new solution strategy of the kinetostatic equations for the unloaded manipulator configuration, which allows computing the stiffness matrix for the overconstrained architectures, including singular manipulator postures. The advantages of the developed technique are confirmed by application examples, which deal with comparative stiffness analysis of two translational parallel manipulators of 3-PUU and 3-PRPaR architectures. Accuracy of the proposed approach was evaluated for a case study, which focuses on stiffness analysis of Orthoglide parallel manipulator.

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Article

The problem of path generation for the spherical 4R mechanism is solved using
the Differential Evolution algorithm (DE). Formulas for the spherical geodesics
are employed in order to obtain the parametric equation for the generated
trajectory. Direct optimization of the objective function gives the solution to
the path generation task without prescribed timing. Therefore, there is no need
to separate this task into two stages to make the optimization. Moreover, the
order defect problem can be solved without difficulty by means of manipulations
of the individuals in the DE algorithm. Two examples of optimum synthesis
showing the simplicity and effectiveness of this approach are included.

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Article

This paper describes a computed-aided design software system for spherical four-bar linkages that is based on Burmester's planar theory. The designer identifies a task in the form of four goal orientations for the floating link and the software generates an array of available linkages known as the type map. The equation of a spherical triangle provides a direct connection to the graphical techniques of Burmester. This paper further develops the linkage type characterization required for an assessment of the resulting designs.

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Article

Joint stiffness of three PUMA 560 manipulators has been measured experimentally. Results of these studies indicate that stiffness data for joints 1, 2 and 3 are similar between PUMA 560 manipulators. Nonlinear relationships between end effector load, end effector displacement and joint configuration are explained. Because mass and inertia data has already been determined, complete dynamic models of the PUMA 560 manipulator which include joint compliance data, are now possible. Using linearized equilibrium equations, static, compliant, configuration dependent joint deflections are determined and compared with experimental results.

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Article

This paper addresses the graphical representation of performances and the optimum design issue of the planar 5R symmetrical parallel mechanism. In this the paper, some performance indices, such as the global conditioning index (GCI), the global velocity index (GVI), the global payload index (GPI), and the global stiffness (deformation) index (GSI), will be defined and investigated. The corresponding atlases will be finally represented graphically in the established design space. Based on these atlases, one can synthesize the link lengths of the studied mechanism with respect to specified criteria. Some examples will be given to show how to use the atlases. Especially, an example will be presented to achieve the optimum dimensional mechanism with respect to a desired workspace based on the optimum non-dimensional result obtained from the atlases. For the reason that using the atlases presented in this paper a designer can obtain the optimum result with respect to any object(s), the optimum design method proposed in this paper can be accepted by others.

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Article

The copious literature dealing with overconstrained linkages shows that this topic is still of great interest. Indeed many questions concerning these “paradoxical” linkages remain unsolved. Furthermore, the increased industrial application of genuine space mechanisms has made it desirable to minimize the number of links.In the present paper a new 6R space mechanism is described, the synthesis of which is achieved by coalescing two appropriate generalized Goldberg 5R linkages. This is done in a manner similar to the synthesis of the Goldberg 5R linkage itself, that is, by blending two Bennett 4R linkages. All five input-output equations are porvided, and some numerical results are presented graphically.ZusammenfassungIn der vorliegenden Arbeit werden zuerst die Übertragungsfunktionen des verallgemeinerten Goldberg 5R Mechanismus angegeben, und sodann die Synthese eines neuen übergeschlossenen 6R Raummechanismus beschrieben, der durch die Vereinigung von zwei geeigneten Goldberg 5R Mechanismen entsteht. Durch Vertauschung einer Gliederfolge (Isomerisation) kann von diesem Mechanismus ein zweiter übergeschlossener 6R Mechanismus abgeleitet werden. Für diese beiden übergeschlossenen Raummechanismen, den Hybrid 6R Mechanismus und dessen Variante, werden sämtliche Übertragungsfunktionen berechnet und numerische Ergebnisse für einen speziellen Systemparametersatz in der Form von Diagrammen mitgeteilt.

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Article

This paper treats the problems of kinematics, singularity and workspace analysis of the 5R symmetrical parallel mechanism. In the design process, the theoretical workspace cannot be used directly due to the inside singularity. The inverse and forward kinematic solutions determine the working and assembly modes of a mechanism. With different modes, a mechanism will have different singular loci and workspaces. In this paper, the singularity and usable workspace without singularity inside will be determined for the mechanism with a specified mode. A concept, the maximal inscribed workspace (MIW) that is bounded by the maximal inscribed circle (MIC), is defined to characterize the workspace performance. A non-dimensional design space is established to investigate the singular loci and workspace shape of the mechanisms, systematically. The atlas of the MIC radius is presented. Based on the obtained distribution charts of the singularity and workspace shape and the atlas, one can know the singularity and workspace performances of any one of the 5R symmetrical parallel mechanisms. The result, especially that of the MIW, of this paper is very useful for the optimum design of the mechanism.

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Article

In this paper we introduce four new posture-dependent performance indices for control. Two of them are based on an object-oriented metric in the workspace (end-effector dependent) and the other on a linearized approximation of direct kinematics (end-effector independent). All newly defined indices are invariant under rigid-body motions and similarities, they have a geometric meaning, and they can be computed in real time. We also give a geometric interpretation of the characteristic length.

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Article

This paper considers the computation of all solutions to the inverse position problem for general six-revolute-joint manipulators. Instead of reducing the problem to one highly complicated input-output equation, we work with a system of 11 very simple polynomial equations. Although the total degree of the system is large (1024), using the “method of the generic case” we show numerically that the generic number of solutions is 16, in agreement with previous works. Moreover, we present an efficient numerical method for finding all 16 solutions, based on coefficient-parameter polynomial continuation. We present a set of 41 test problems, on which the algorithm used an average of less than 10 s of CPU time on an IBM 370–3090 in double precision FORTRAN. The methodology applies equally well to other problems in kinematics that can be formulated as polynomial systems.

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Article

A closed 6R linkage is generically rigid. Special cases may be mobile. Many
families of mobile 6R linkages have been characterised in terms of the
invariant Denavit-Hartenberg parameters of the linkage. In other words, many
sufficient conditions for mobility are known. In this paper we give, for the
first time, equational conditions on the invariant Denavit-Hartenberg
parameters that are necessary for mobility. The method is based on the theory
of bonds. We illustrate the method by deriving the equational conditions for
various well-known linkages (Bricard's line symmetric linkage, Hooke's linkage,
Dietmaier's linkage, and recent a generalization of Bricard's orthogonal
linkage), starting from their bond diagrams; and by deriving the equations for
another bond diagram, thereby discovering a new mobile 6R linkage.

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Article

In this paper a new and very efficient algorithm to compute the inverse kinematics of a general 6R serial kinematic chain is presented. The main idea is to make use of classical multidimensional geometry to structure the problem and to use the geometric information before starting the elimination process. For the geometric pre-processing we utilize the Study model of Euclidean displacements, sometimes called kinematic image, which identifies a displacement with a point on a six dimensional quadric in seven dimensional projective space P7. The 6R-chain is broken up in the middle to form two open 3R-chains. The kinematic image of a 3R-chain turns out to be a Segre-manifold consisting of a one parameter set of 3-spaces. The intersection of two Segre-manifolds and yields 16 points which are the kinematic images representing the 16 solutions of the inverse kinematics. Algebraically this procedure means that we have to solve a system of seven linear equations and one resultant to arrive at the univariate 16 degree polynomial. From this step in the algorithm we get two out of the six joint angles and the remaining four angles are obtained straight forward by solving the inverse kinematics of two 2R-chains.

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Article

This paper presents an original use of Evolutionary Algorithms in order to approximate by a closed form the inverse kinematic model (IKM) of analytical, non-analytical and general (i.e. with an arbitrary geometry) manipulators. The objective is to provide a fast and general solution to the inverse kinematic problem when it is extensively evaluated as in design processes of manipulators. A mathematical function is evolved through Genetic Programming according to the known direct kinematic model to determine an analytical expression which approximates the joint variable solution for a given end-effector configuration. As an illustration of this evolutionary symbolic regression process, the inverse kinematic models of the PUMA and the GMF Arc Mate are approximated before to apply the algorithm to general 6R manipulators.

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Article

In this paper, we consider a special kind of overconstrained 6R closed linkage which we call angle-symmetric 6R linkage. These are linkages with the property that the rotation angles are equal for each of the three pairs of opposite joints. We give a classification of these linkages. It turns out that there are three types. First, we have the linkages with line symmetry. The second type is new. The third type is related to cubic motion polynomials.

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Article

An original model is set up which incorporates the contribution of tooth wear in quasi-static and dynamic simulations of wide-faced solid spur and helical gears. Considering mild abrasive wear, Archard’s law is used and the influence of the lubrication regime is included. Wear is accounted for via time and position varying distributions of normal deviations with respect to ideal flank geometry which are superimposed on profile and lead modifications. A time-step integration scheme combined with a contact algorithm is used to solve the equations of motion. The numerical results show that, for wide-faced gears, wear is asymmetric in the lead direction and can progressively improve load distribution. Wear seems generally detrimental to helical gear dynamic behaviour whereas, for uncorrected spur gears, it can be beneficial in terms of vibrations as it acts to a certain extent as profile relief. In the case of spur gears, wear appears as a dynamic phenomenon which interacts with gear vibrations as shown by transmission errors which are dependent on wear.

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Article

Stability characteristics in principal and combination parametric resonance of an axially accelerating string supported by a partial elastic foundation are analytically investigated. The model is considered as a three part system; one is subjected to an elastic foundation, and two are free to vibrate. The equations of orders one and epsilon are derived using the method of multiple scales (MMS). The axial velocity is assumed to be a mean velocity, along with small harmonic fluctuations. The mode shapes and natural frequencies of the system are derived using the equation of order one, and satisfying the compatibility conditions between three segments of the string. For the principal and combination resonance cases, including summation and difference types, the stability conditions are investigated analytically. Eventually, the effects of system parameters on natural frequencies and stability boundaries of the system are presented through numerical simulations.

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