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A new kinematic design methodology is presented for optimization of spherical serial mechanisms. This method integrates multiple criteria (workspace, manipulability, and size) linearly in one objective function. All these criteria are optimized simultaneously to lead to a more realistic solution. By changing the priorities of each criterion, different sets of desirable kinematic performance can be expressed. The global manipulability and the uniformity of manipulability over the workspace are combined in a single index to improve the synthesis results. The optimization result for a spherical bevel-geared mechanism using a genetic algorithm demonstrated that the proposed method effectively improves the quality of the optimum solution and provides insight into the workings of the mechanism. In addition, this flexible and adaptable methodology may also be extended for use in general optimization for linkage synthesis.

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... Path and motion planning are generally expressed in the Cartesian frame, the control is performed relative to the joint-frames. IK produces the motions of the joints in accordance with the needed Cartesian path or trajectory [33,46]. For this class of application several techniques for solving IK was investigated, due to the complexity of the analytical solutions essentially when the system has a high number of Degrees of Freedom, DOF. ...

... In heuristic based IK solver we can identify two main classes: Computational based techniques and learning based techniques. The first class is based on nature inspired heuristics such as Particle Swarm Optimization, PSO [25,26,40], Ant Colony Optimization, ACO [20], Genetic Algorithms, GA [12,46]; Buckley et al. [4] or Ant Bee Colony, ABC [6]. For these methods, the IK problem is addressed as an optimization and the heuristics is used as computing alternatives. ...

... In inverse kinematics based on PSO [25]; or on GA such as [4,12,46], a stochastic search is performed, using a population in GA or a set of individuals in PSO, ABC and ACO; each population or individual is a possible solution, here a set of joints positions of the IK problem. Any possible solution is ranked, using a fitness function and the best is returned as the solution of the problem, for a given input, here a target position. ...

In this paper, a heuristic method based on Firefly Algorithm is proposed for inverse kinematics problems in articulated robotics. The proposal is called, IK-FA. Solving inverse kinematics, IK, consists in finding a set of joint-positions allowing a specific point of the system to achieve a target position. In IK-FA, the Fireflies positions are assumed to be a possible solution for joints elementary motions. For a robotic system with a known forward kinematic model, IK-Fireflies, is used to generate iteratively a set of joint motions, then the forward kinematic model of the system is used to compute the relative Cartesian positions of a specific end-segment, and to compare it to the needed target position. This is a heuristic approach for solving inverse kinematics without computing the inverse model. IK-FA tends to minimize the distance to a target position, the fitness function could be established as the distance between the obtained forward positions and the desired one, it is subject to minimization. In this paper IK-FA is tested over a 3 links articulated planar system, the evaluation is based on statistical analysis of the convergence and the solution quality for 100 tests. The impact of key FA parameters is also investigated with a focus on the impact of the number of fireflies, the impact of the maximum iteration number and also the impact of (α, β, γ, δ) parameters. For a given set of valuable parameters, the heuristic converges to a static fitness value within a fix maximum number of iterations. IK-FA has a fair convergence time, for the tested configuration, the average was about 2.3394 × 10−3 seconds with a position error fitness around 3.116 × 10−8 for 100 tests. The algorithm showed also evidence of robustness over the target position, since for all conducted tests with a random target position IK-FA achieved a solution with a position error lower or equal to 5.4722 × 10−9.

... H. Shao et al. proposed a new global dynamic conditioning index which evaluates the inertia matrix of the dynamics model of the manipulator that shows the nature of workspace during its motion [23]. X. Zhang proposed some new dexterity measures which show the uniformity and consistency of the condition and isotropy in the given workspace [24]. I. Mansouri et al. proposed power as the new measure of homogeneous manipulability of the robot manipulator and formed a power ellipsoid that is a function of task space force and velocity transmissibility [25]. ...

... By sampling the whole workspace, an average of discrete sum of the isotropic index is obtained for all sampled position. So, the numerical form is given by [24] ...

... The global dexterity index is advantageous in maximizing the average value of manipulability for the whole workspace but it might be of least concern in minimizing the poor singular behavior over the surface of workspace. The uniformity of manipulability index describes the variation of relative dexterous behavior [24]. A design with good uniformity index could be a good candidate for defining the efficient trajectories during surgical procedures. ...

Efficient minimally invasive surgeries greatly depend on dexterous workspace in which surgeon feels great comfort incorporating his skills. Serial Haptic Master devices with large DOF have advantages of large workspace and improved dexterity but these also contribute more to the kinematic errors and dynamics effects if not properly designed. Consequently, improper transmission of forces from surgeon could result in damaging delicate tissues in the surrounding of surgical site. This paper provides workspace analysis and optimization of the 4 links of an 8 DOF Haptic Master device that minimizes the kinematics errors during its manipulation, ultimately improves the efficiency of surgical procedures. Complete kinematics of the device is calculated. A cost function is defined that uses a global performance index to provide uniform dexterous workspace for effective force transmissibility in surgical environment and then optimization of 4 link lengths is carried out on the basis of defined cost function. Analysis of efficient trajectories is made on the basis of optimization results.

... 析法求解 4、5 组给定角度关系的问题。ALIZADE 等 [2] 给出求解 5 组给定关系精确综合问题的线性方 程组，降低了计算难度。CERVANTES-SÁNCHEZ 等 [3][4] 应用解析法研究 3～6 组给定关系的精确综合 问题，其 6 组给定角度关系综合问题的求解方程为 10 次多项式。杨通等 [5] 给出 4 组给定关系的球面 Burmester 曲线方程及 Burmester 点的计算和分类方 法，进而得出精确综合问题的机构类型解域。 在近似函数发生综合方面，LIU 等 [6] 建立可动 性约束下的最小二乘优化模型，再应用正交解耦算 法求解该问题。尔后，他们进一步研究这类问题 [7] ， 先规划出输入-输出曲线并据此选择数据， 再应用优 化程序使其误差最小化。FARHANG 等 [8] 应用曲柄 转角的一次和二次谐波线性组合函数，建立从动连 架杆转角的近似表达式，由该近似方程综合出具有 整转运动的机构。王德伦等 [9] 应用自适应近似综合 理论和鞍点规划方法研究近似函数综合问题，得到 较好结果。ALIZADE 等 [10] 应用内点插值、最小二 乘和 Chebyshev 近似法研究函数综合问题，并对 3 种方法的求解结果进行对比分析。褚金奎等 [11] 应用 Fourier 变换理论研究该问题，提出近似函数综合的 数值图谱方法。 ALIZADEH 等 [12] 研究了机架中心角 为 90°的两连架杆准等速设计问题，将其转化为最 小化设计误差或结构误差的近似函数综合问题。 随着计算智能技术的发展，现代智能算法越来 越 广 泛 地 应 用 于 连 杆 机 构 尺 度 综 合 及 构 型 优 选 [13][14][15][16][17][18][19][20][21] 。LIU 等 [13] 在曲线形状特征参数提取的基础 上，应用人工免疫系统求解铰链四杆机构轨迹生成 问题。SMAILI 等 [14] 建立具有混合任务的铰链四杆 机构近似运动学优化设计模型，再应用融合蚁群算 法与梯度搜索的混合方法求解该问题。段旭洋等 [15] 应用嵌套粒子群算法综合四、六和八杆轨迹生成机 构，并进行构型优选；ZHAO 等 [16] 则应用粒子群算 法对重载操作机多杆机构进行构型优选。LIN [17] 设 计一种遗传算法和差分进化(Differential evolution, DE)混合算法，再应用于铰链四杆机构轨迹优化综 合中。车林仙 [18] 应用双种群 DE 算法求解铰链四杆 机构近似运动学优化设计模型。ORTIZ 等 [19] 设计一 种具有自适应控制参数的 DE 算法，再应用于四、 六杆轨迹生成机构优化综合。BULATOVIĆ 等 [20] 应 用新颖的布谷鸟搜索算法求解六杆双停歇机构优化 综合问题。ZHANG 等 [21] 提出球面串联机构的多准 则运动学优化方法，将关于工作空间、可操作性指 标和机构尺寸的多目标优化问题，通过线性加权转 化为单目标优化问题， 再应用遗传算法求解该问题， 有效改进优化解的质量。 [24] 和ε-DE 算法 [25] 等近年来提出的有效改 进算法比较。 将球面四杆机构优化综合问题的约束条件分 为软、硬条件 [18] ，并分类处理，形成面向机构优化 综合的带修复策略的 FRDE 算法(FRDE algorithm with repair strategies, FRRDE)。最后，给出 5 个机构 综合实例，以验证 FRRDE 算法的有效性和可靠性。 1 球面四杆机构近似函数综合 数学模型 ...

... 析法求解 4、5 组给定角度关系的问题。ALIZADE 等 [2] 给出求解 5 组给定关系精确综合问题的线性方 程组，降低了计算难度。CERVANTES-SÁNCHEZ 等 [3][4] 应用解析法研究 3～6 组给定关系的精确综合 问题，其 6 组给定角度关系综合问题的求解方程为 10 次多项式。杨通等 [5] 给出 4 组给定关系的球面 Burmester 曲线方程及 Burmester 点的计算和分类方 法，进而得出精确综合问题的机构类型解域。 在近似函数发生综合方面，LIU 等 [6] 建立可动 性约束下的最小二乘优化模型，再应用正交解耦算 法求解该问题。尔后，他们进一步研究这类问题 [7] ， 先规划出输入-输出曲线并据此选择数据， 再应用优 化程序使其误差最小化。FARHANG 等 [8] 应用曲柄 转角的一次和二次谐波线性组合函数，建立从动连 架杆转角的近似表达式，由该近似方程综合出具有 整转运动的机构。王德伦等 [9] 应用自适应近似综合 理论和鞍点规划方法研究近似函数综合问题，得到 较好结果。ALIZADE 等 [10] 应用内点插值、最小二 乘和 Chebyshev 近似法研究函数综合问题，并对 3 种方法的求解结果进行对比分析。褚金奎等 [11] 应用 Fourier 变换理论研究该问题，提出近似函数综合的 数值图谱方法。 ALIZADEH 等 [12] 研究了机架中心角 为 90°的两连架杆准等速设计问题，将其转化为最 小化设计误差或结构误差的近似函数综合问题。 随着计算智能技术的发展，现代智能算法越来 越 广 泛 地 应 用 于 连 杆 机 构 尺 度 综 合 及 构 型 优 选 [13][14][15][16][17][18][19][20][21] 。LIU 等 [13] 在曲线形状特征参数提取的基础 上，应用人工免疫系统求解铰链四杆机构轨迹生成 问题。SMAILI 等 [14] 建立具有混合任务的铰链四杆 机构近似运动学优化设计模型，再应用融合蚁群算 法与梯度搜索的混合方法求解该问题。段旭洋等 [15] 应用嵌套粒子群算法综合四、六和八杆轨迹生成机 构，并进行构型优选；ZHAO 等 [16] 则应用粒子群算 法对重载操作机多杆机构进行构型优选。LIN [17] 设 计一种遗传算法和差分进化(Differential evolution, DE)混合算法，再应用于铰链四杆机构轨迹优化综 合中。车林仙 [18] 应用双种群 DE 算法求解铰链四杆 机构近似运动学优化设计模型。ORTIZ 等 [19] 设计一 种具有自适应控制参数的 DE 算法，再应用于四、 六杆轨迹生成机构优化综合。BULATOVIĆ 等 [20] 应 用新颖的布谷鸟搜索算法求解六杆双停歇机构优化 综合问题。ZHANG 等 [21] 提出球面串联机构的多准 则运动学优化方法，将关于工作空间、可操作性指 标和机构尺寸的多目标优化问题，通过线性加权转 化为单目标优化问题， 再应用遗传算法求解该问题， 有效改进优化解的质量。 [24] 和ε-DE 算法 [25] 等近年来提出的有效改 进算法比较。 将球面四杆机构优化综合问题的约束条件分 为软、硬条件 [18] ，并分类处理，形成面向机构优化 综合的带修复策略的 FRDE 算法(FRDE algorithm with repair strategies, FRRDE)。最后，给出 5 个机构 综合实例，以验证 FRRDE 算法的有效性和可靠性。 1 球面四杆机构近似函数综合 数学模型 ...

... Here mech anisms which can potentially achieve a given task are sought. Many search methods have been proposed to deal with the synthesis problem (for example [12,13,14,15]). These use optimization techniques to change a given mech anism to one which more accurately generates a prescribed path, usually a coupler path. ...

... Table 2 gives the resultant points and they are also shown in figure 6. Figure 6: Views of points around 3D path from [25] normalized to lie on unit sphere improve the match between the path that is obtained by the selection from the atlas and what is required. The improvement step is that suggested in part 8 of figure 4. A number of methods for undertaking such improvement have appeared in the literature (for example [12,13,14,15]). These use various optimization schemes to try to improve a suitable measure of the goodness of fit between the path generated by a candidate mechanism and given precision points. ...

An atlas or catalogue of mechanisms provides a useful aid in the synthesis of mechanisms for new applications. The atlas stores mechanisms together with their coupler paths. Fourier techniques can be used as a convenient means for representing, in normalized form, curves for planar mechanisms. This paper looks at the extension to spherical four-bar mechanisms. In particular, a means for projecting a spherical curve onto a plane is discussed which depends only on the geometry of the curve and not on the choice of world coordinate system.

... The principle of the comprehensive objective method is to define the sum of the weights of multiple performance indices as a comprehensive index (the sum of the weight factors is equal to 1) [146,162,196]. Its advantage is that a global optimum can finally be obtained and is easy to implement. ...

In this chapter, we focus on the stiffness performance evaluation and optimization design of parallel manipulators (PMs), the comprehensive stiffness index (CSI) that separates the linear stiffness and angular stiffness and considers the effect of the coupling of the non-diagonal elements is introduced, as well as the extreme stiffness index.

... The principle of the comprehensive objective method is to define the sum of the weights of multiple performance indices as a comprehensive index (the sum of the weight factors is equal to 1) [146,162,196]. Its advantage is that a global optimum can finally be obtained and is easy to implement. ...

Since the parallel manipulators (PMs) have excellent dynamic performance, high agility.

... The principle of the comprehensive objective method is to define the sum of the weights of multiple performance indices as a comprehensive index (the sum of the weight factors is equal to 1) [146,162,196]. Its advantage is that a global optimum can finally be obtained and is easy to implement. ...

In the optimization design mathematical model, dimensions are always concerned as variables, but it is noted that a mechanism especially PM may associate with amount of dimensions.

Over the last few decades, PMs with actuation redundancy have attracted increasing attention in both academia and industry.

The traditional multi-objective optimization design methods of parallel manipulators (PMs) mainly include the comprehensive objective method (Wang and Zhang in Mech. Mach. Theory 112:61–83, 2017) and the Pareto frontier method (STAN et al. in Potentialities of optimal design methods for the development of mini parallel robots using genetic algorithms, vols 1–6, pp 1591–1596 2007).

It is necessary to obtain more non-dominated solutions for multi-objective optimization design of parallel manipulators (PMs) in actual engineering environment, the traditional optimization design method achieves this goal by increasing the number of population size, and however, this leads to an exponential increase in computational cost.

Kinematic performance analysis and optimization of PMs are essential for the actual design and control, which have attracted increasing attention in both academia and industry.

Performance optimization of parallel manipulators (PMs) have attracted adequate attention in recent years. It mainly concerns performance indices, optimization algorithms and optimization methods. This paper presents an in-depth, comprehensive, reasoned overview for the three basic issues. The research status and existing problems of these issues along with the distinctive approaches that have been explored are reported. Advantages, disadvantages, application scenarios and recommendations of various performance indices, optimization algorithms and methods are discussed. Focus is also placed on future research trends. The results are useful for researchers and engineers to properly select performance indices, optimization algorithms, and optimization methods when designing a PM.

... Merchan et al. [17] applied an optimization process for the synthesis of a polycentric knee prosthesis based on Watt's six-bar linkage planar mechanism. Zhang and Nelson [30] implemented a multi-objective kinematical optimization process in the design of a serial spherical mechanism using genetic algorithms. Cabrera et al. [2] presented a comparative study for the synthesis of four and six bar mechanisms utilizing different strategies by means of an improved algorithm based on the one presented in [3]. ...

... GA is also used in [24] for optimizing multiple criteria of the kinematic design of spherical serial mechanisms. Conceptual design, fuzzy set methods and mechatronic indices are all used in the mechatronic design of robot grippers for handling fabrics in [25]. ...

In this work, we present a generic approach to optimize the design of a parametrized robot gripper including both selected gripper mechanism parameters, and parameters of the finger geometry. We suggest six gripper quality indices that indicate different aspects of the performance of a gripper given a CAD model of an object and a task description. These quality indices are then used to learn task-specific finger designs based on dynamic simulation. We demonstrate our gripper optimization on a parallel finger type gripper described by twelve parameters. We furthermore present a parametrization of the grasping task and context, which is essential as an input to the computation of gripper performance. We exemplify important aspects of the indices by looking at their performance on subsets of the parameter space by discussing the decoupling of parameters and show optimization results for two use cases for different task contexts. We provide a qualitative evaluation of the obtained results based on existing design guidelines and our engineering experience. In addition, we show that with our method we achieve superior alignment properties compared to a naive approach with a cutout based on the “inverse of an object”. Furthermore, we provide an experimental evaluation of our proposed method by verifying the simulated grasp outcomes through a real-world experiment.

... Location of orifice plays a critical role in determining these properties of the arm during surgery [6]. Conventionally, the design of robotic arms is optimized for large workspace and dexterity, neglecting the number of orifices through which these are achievable [7, 8, 9]. Hence, it might be the case that the desired volume of the reachable workspace is achievable through a very limited number of orifices. ...

In minimally invasive robotic surgery (MIRS), a surgeon teleoperates a robotic arm from a master console. This arm operates inside the patient's body through a small orifice which constrains the end-effector's translation along two axes. The workspace of such a robotic arm depends on its design as well as orifice location. Conventionally, the design of such an arm is optimized for large workspace and high dexterity. However, this large workspace might be reachable through only a few orifices, thus making the workspace volume and operation quite sensitive to the orifice location. To overcome this problem, we optimized the design of a 3 degrees of freedom serial robotic arm to attain multiple adjacent (desired number of) possible orifice locations, through which a planar workspace of pre-specified geometry can be traced. To achieve this goal, an algorithm was developed to relate the design of such an MIRS arm to the possible orifice positions. The optimization problem was solved using several metaheuristics such as simulated annealing, Tabu search, artificial bee colonization and genetic algorithm, and their performance was compared.

... Stock et al. proposed a method using search minimization to optimize kinematic design of linear Delta robot [9]. Zhang et al. applied genetic algorithms for the multiple-criteria kinematic optimization of spherical serial mechanisms [10]. Stan et al. presented the optimal design of 3-DOF DELTA linear translation parallel robot also based on genetic algorithm approach [11]. ...

The purpose of this research work is to find the optimized kinematic structural parameters of the 3-TPS/TP parallel manipulator while taking into consideration the workspace, kinematic properties and other factors. The Ranked Pareto Particle Swarm Optimization (RP-PSO) approach is applied to solve the multi-objective optimization problems. Firstly, the structure of the parallel manipulator and its kinematic model are devised. Then, we set up the kinematical performance indices for the evaluation of manipulator working properties, including Local Condition Index (LCI), Global Condition Index (GCI) and Good Condition Workspace (GCW). The optimization is further carried out in a Parameter Design Space (PDS) with normalized geometry parameters. Then the geometry optimization problems are solved using a PDS based RP-PSO approach. Finally, the feasibility of this approach is supported by examples given this paper.

... CoBRASurge (Compact Bevel-geared Robot for Advanced Surgery) [22], [23] is used as the robotic laparoscope holder, shown in the Fig. 1 & 2. It is based on a spherical bevel geared mechanism consisting of three gear pairs and six turning pairs. CoBRASurge creates a mechanically constrained remote center of motion (RCM), which contains three rotational degrees of freedom (DOFs) and one translational DOF passing through it. ...

Current laparoscopic surgeries suffer from inconvenient, limited visualization due to the small incisions. It normally needs an assistant to hold and readjust a laparoscope to view the surgical set when performing procedures. This assistant can be either a human or a robotic laparoscope holder. However, at the current state, both of them only passively follow the control commands from the surgeon (The human assistant relies on the surgeon's verbal communications and the robotic holder is controlled by the voice or joystick/buttons), whenever the laparoscope needs to be readjusted. The surgeon's explicit intervention in laparoscope readjustment might bring extra mental and physical burdens to him/her. In this paper, the work of granting attention-awareness to a robotic laparoscope holder is presented. The robot can actively observe the surgeon's viewing attention by tracking the surgeon's eye movements and automatically adjust the laparoscope's view correspondingly. Our experimental results demonstrated that this system effectively released the surgeon from the intervention of the laparoscope, which could eliminate the visualization barriers of laparoscopic surgeries, reduce the learning curve in laparoscopic surgeries, and reduce the operation time and cost.

... System designers are obliged to develop mapping functions from the workspace of the master device to that of the slave device. Since exact mapping functions do not generally exist, designers adopts various optimization methods, which are widely used in mechanical design, including determination of the boundary of manipulator workspace [11], maximization of the dexterous regular workspace [12], optimization of joint stiffness of robotic arms [13], and design of the spherical serial manipulators [14]. ...

The complex kinematic structure of a human thumb makes it difficult to capture and control the thumb motions. A further complication is that mapping the fingertip position alone leads to inadequate grasping postures for current robotic hands, many of which are equipped with tactile sensors on the volar side of the fingers. This paper aimed to use a data glove as the input device to teleoperate the thumb of a humanoid robotic hand. An experiment protocol was developed with only minimum hardware involved to compensate for the differences in kinematic structures between a robotic hand and a human hand. A nonlinear constrained-optimization formulation was proposed to map and calibrate the motion of a human thumb to that of a robotic thumb by minimizing the maximum errors (minimax algorithms) of fingertip position while subject to the constraint of the normals of the surfaces of the thumb and the index fingertips within a friction cone. The proposed approach could be extended to other teleoperation applications, where the master and slave devices differ in kinematic structure.

... Then, 16 solutions were obtained from resultant matrix via linear algebra and Dixion resultant elimination. In addition, detailed descriptions of other methods have been given [8][9][10][11][12]. However, such methods suffer from complex matrix calculations, high computational cost and severe singularity as the number of robot DOFs increases and may not guarantee the requirement for real-time and position accuracy. ...

In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.

This paper explores the simulation-based design optimization of a variable geometry spray (VGS) fuel injector. A multi-objective genetic algorithm (MOGA) is interfaced with commercial computational fluid dynamics (CFD) software and high performance computing capabilities to evaluate the spray characteristics of each VGS candidate design. A three-point full factorial experimental design is conducted to identify significant design variables and to better understand possible variable interactions. The Pareto frontier of optimal designs reveals the inherent tradeoff between two performance objectives-actuator stroke and spray angle sensitivity. Analysis of these solutions provides insight into dependencies between design parameters and the performance objectives and is used to assess possible performance gains with respect to initial prototype configurations. These insights provide valuable design information for the continued development of this VGS technology.

This paper deals with an optimization method of spherical robots applied to the domain of medical robotics. This method relies on specification of indices which describe the constraints and requirements of the particular medical application. The dimensional optimization is demonstrated with two examples of four-degree-of-freedom robots: one dedicated to ultrasound tele-echography and the other a tool for minimally invasive surgery. Each of them has been designed to accurately follow medical gestures. The method involves optimization of the kinematic structure and determination of geometric parameters which have a significant role in avoiding singularities and achieving mechanism compactness. The two examples presented illustrate the robustness of the approach using specialized indices appropriate to each specific case. The method can be used with some generality for new medical robotics applications.

This paper focuses on the geometry optimization of a 3-TPS/TP parallel manipulator with Parameter Design Space (PDS). Firstly, the structure of the parallel manipulator and its kinematic model are presented. Then, we set up the kinematical performance indices for the evaluation of manipulator working properties, including Local Condition Index (LCI), Global Condition Index (GCI) and Good Condition Workspace (GCW). The optimization objective of this research is to get a larger workspace with good condition. The optimization has been carried out in a PDS with normalized geometry parameters. Three dimensional performance charts and two dimensional atlases are then generated for the performance indices. An optimum region with all optimum solutions are then generated from the atlases. The feasibility of this approach is supported by the example given this paper.

This paper deals with processes of optimisation for the design of a four degree-of-freedomrobot dedicated to remote ultrasound tele-echography. This robot is designed to track the medical gestures of a remote expert moving an ultrasound probe. The goal is to optimise the kinematic structure by fixing the geometric parameters; these have a significant role in robot configuration singularities, with respect to current medical gestures and mechanism compactness. After choosing a dedicated kinematic structure, several optimisations are presented. Then, an optimal choice of geometrical parameters of a global function in relation with kinematic performance indices and compactness is proposed. This robot is soon to be used in the experimental medical phase of the Prosit project.

This paper is concerned with the determination of optimum forces extracted by robot grippers on the surface of a grasped rigid object -- a matter which is crucial to guarantee the stability of the grip without causing defect or damage to the grasped object. A multi-criteria optimization of robot gripper design problem is solved with two different configurations involving two conflicting objectives and a number of constraints. The objectives involve minimization of the difference between maximum and minimum gripping forces and simultaneous minimization of the transmission ratio between the applied gripper actuator force and the force experienced at the gripping ends. Two different configurations of the robot gripper are designed by a state-of-the-art algorithm (NSGA-II) and the obtained results are compared with a previous study. Due to presence of geometric constraints, the resulting optimization problem is highly non-linear and multi-modal. For both gripper configurations, the proposed methodology outperforms the results of the previous study. The Pareto-optimal solutions are thoroughly investigated to establish some meaningful relationships between the objective functions and variable values. In addition, it is observed that one of the gripper configurations completely outperforms the other one from the point of view of both objectives, thereby establishing a complete bias towards the use of one of the configurations in practice.

In this paper, the physical model of the solution space of spherical 3-DOF serial wrists is established. The reachable workspaces are classified. The dexterous workspaces for such wrists are investigated based on the rotatability conditions for the spherical 4-bar mechanism. Using the theory of conformal transformation, we obtain plane figures of the reachable and dexterous workspaces. The atlases of the workspaces in the physical model of the solution space are plotted. These results are useful not only for designer overall to understand the relationship between the workspaces and link lengths of spherical 3-DOF serial wrists, but also for the design of the wrists.

This paper presents a new approach to using virtual reality (VR) to design spherical mechanisms. VR provides a three-dimensional (3-D) design space where a designer can input design positions using a combination of hand gestures and motions and view the resultant mechanism in stereo using natural head movement to change the viewpoint. Because of the three-dimensional nature of the design and verification of spherical mechanisms, VR is examined as a new design interface in this research. In addition to providing a VR environment for design, the research presented in this paper has focused on developing a "design in context" approach to spherical mechanism design. Previous design methods have involved placing coordinate frames along the surface of a constraint sphere. The new "design in context" approach allows a designer to freely place geometric models of movable objects inside an environment consisting of fixed objects. The fixed objects could either act as a base for a mechanism or be potential sources of interference with the motion of the the mechanism. This approach allows a designer to perform kinematic synthesis of a mechanism while giving consideration to the interaction of that mechanism with its application environment.

The spherical 5R parallel manipulator is a typical parallel manipulator. It can be used as a pointing device or as a minimally invasive surgical robot. This study addresses the motion/force transmission analysis and optimization of the manipulator by taking into account the motion/force transmissibility. The kinematics of the manipulator is analyzed. Several transmission indices are defined by using screw theory for the performance evaluation and dimensional synthesis. The process of determining the optimal angular parameters based on performance charts is presented. The manipulator that has a large workspace and good motion/force transmissibility is identified.

The article describes the design of a robotic wrist able to perform spherical motions: its mechanical architecture is based on parallel kinematics and is suitable to be realized at the mini-or micro-scale by means of flexible joints. In view of the preliminary design, a rigid body model has been studied first and the direct and inverse kinematic analyses have been performed, allowing for the determination of theoretical workspace and passive joints displacements. The rigid body dynamic behavior and the operative ranges of the machine have been assessed through the development of an inverse dynamics model. Then, the micro parts have been designed with the help of FEM and multibody software and the study has been focused on the flexures: since the analyses showed that the centre of the spherical motion moves around several millimeters in the workspace, the original kinematic concept has been modified with the introduction of a ball joint constraining the mobile platform to frame so as to prevent unwanted translations.

This paper addresses an optimal study of workspace for spherical parallel mechanism for laparoscopic surgery. The spherical parallel manipulator has been selected because of its characteristics. Two designs have been studied for maximizing their workspaces; a haptic device, as part of training system, and a laparoscope holding mechanism. The laparoscope holding mechanism has to satisfy additional constraints by minimizing the occupied space above the patient. The objective is to solve design problem to offer the maximal workspace for such mechanisms. The design of a haptic interface and the laparoscope holding mechanism based on the optimal parameters are presented. This paper presents a Genetic Algorithm (GA) approach for selecting optimal design parameters for maximizing workspace of spherical parallel mechanism.

A kinematic is presented that is fully parallel and actuator
redundant. Actuator redundancy refers to the use of more actuators than
are strictly necessary to control the mechanism without increasing the
mobility. The uses of this form of redundancy include the ability to
partially control the internal forces, increase the workspace, remove
singularities, and augment the dexterity. Optimization takes place based
on several objective functions. The kinematic dexterity, the forces
present at the actuators, and the uniformity of the dexterity over the
workspace are all investigated as potential objectives. Global measures
are derived from each of these quantities for optimization purposes.
Instead, optimization of several factors is done simultaneously by
specifying a primary objective and minimum performance standards for the
secondary measures

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.

The size and limited dexterity of current surgical robotic systems are factors which limit their usefulness. To improve the level of assimilation of surgical robots in minimally invasive surgery (MIS), a compact, lightweight surgical robotic positioning mechanism with four degrees of freedom (DOF) (three rotational DOF and one translation DOF) is proposed in this paper. This spatial mechanism based on a bevel-gear wrist is remotely driven with three rotation axes intersecting at a remote rotation center (the MIS entry port). Forward and inverse kinematics are derived, and these are used for optimizing the mechanism structure given workspace requirements. By evaluating different spherical geared configurations with various link angles and pitch angles, an optimal design is achieved which performs surgical tool positioning throughout the desired kinematic workspace while occupying a small space bounded by a hemisphere of radius 13.7 cm. This optimized workspace conservatively accounts for collision avoidance between patient and robot or internally between the robot links. This resultant mechanism is highly compact and yet has the dexterity to cover the extended workspace typically required in telesurgery. It can also be used for tool tracking and skills assessment. Due to the linear nature of the gearing relationships, it may also be well suited for implementing force feedback for telesurgery.

A novel spherical gripper mechanism (SGM) with one degree of freedom was designed. This gripper consists of a network of spherical parallelogram mechanisms. Design limits, work space formulae, and required grasping forces are derived. Parallelogram mechanisms with unequal circular and spiral linkages are also investigated. It is shown that the spherical parallelogram mechanisms with spiral linkages may be used for grasping objects.

The multiobjective optimization of a four-degree-of-freedom symmetric parallel manipulator for Schönflies-motion generation is the subject of this paper. First, the inverse positioning problem is discussed, along with its velocity analysis. The workspace is then analyzed, thereby deriving a closed-form expression of the workspace volume, which depends on the orientation of the moving platform. Next, the isotropic design of the manipulator is obtained. Then, the dexterity analysis of the manipulator is conducted, which is one objective of the optimum design of the manipulator, a second objective being a normalized workspace volume. Finally, the results of the optimization process are reported in terms of a set of Pareto-optimum pairs of the design parameters.

An atlas of topological and functional representations of bevel gear-type basic robotic wrists of up to nine links with all the actuators connected to the frame link is presented. Each wrist mechanism is depicted by means of a canonical diagram that can be adopted as a schematic model for the final constructive embodiment. The corresponding graphic representation is also shown, together with a reference number that classifies the structure through the concepts of nonfractionated degree of freedom and equivalent-open-loop chain.

The analysis on the workspace and rotational capability of HANA, a spatial 3-DoF parallel manipulator, is concerned. The parallel manipulator consists of a base plate, a movable platform, and three connecting legs. The moving platform has three degrees of freedom (DoFs) which are two translations and one rotation, with respect to the base plate. The new parallel manipulator is very interesting for the reason of no singularity in the workspace, the single-DoF joint architecture and high rotational capability of the moving platform. The inverse kinematics problem is described in a closed-form, which is very useful to present the workspace geometrically. The constant-orientation and reachable workspaces for the manipulator are analyzed firstly. The index that is used to evaluate the rotational capability of the manipulator is defined and discussed in detail. Finally, the distribution of rotational capability index on the workspace is presented, which helps us know how much the index is at different point. The parallel manipulator has wide application in the fields of industrial robots, simulators, micro-motion manipulators, and parallel kinematics machines.

In the paper, the algorithm of designing some geometrical parameters of a Delta parallel manipulator has been described. The manipulator is to work in a specified workspace, which is given as a set of points. The first step of the algorithm seeks the possible solutions, and because there are an infinite number of them, the objective of the second step is to limit the number by an optimization. Owing to this, it is possible to find parameters of the manipulator, whose workspace contains the specified points. © 2003 Wiley Periodicals, Inc.

This paper addresses the general issue of optimal kinematic design of parallel mechanisms. Optimal design is one of the most challenging issues in the field. To solve the design problem ideally, the difficulties that one should solve can be summarized as: (a) reducing the number of design parameters; (b) specifying the bounds of each parameter reasonably; (c) defining a parameter design space, in which the optimal kinematic design can be implemented logically; (d) providing all possible optimal results. This paper proposes an optimal kinematic design methodology, which is referred to as Performance-Chart based Design Methodology (PCbDM), for parallel mechanisms with fewer than five linear parameters. Some steps in this methodology are also helpful for the objective-function based optimal design. The results of this paper will be very useful in developing the computer-aided design system for parallel mechanisms. The proposed design methodology can be also applied in serial and parallel robots or any other mechanisms.

This paper exploits a new algorithm to optimize the length of the legs of a spatial parallel manipulator for the purpose of obtaining a desired dexterous workspace rather than the whole reachable workspace. With the analysis of the degree of freedom (DoF) of a manipulator, we can select the least number of variables to depict the kinematic constraints of each leg of a manipulator. The optimum parameters can be obtained by searching the extreme values of the objective functions with the given adroit workspace. Example is utilized to demonstrate the significant advantages of this method in the dexterous workspace synthesis. In applications, this method can be widely used to synthesize, optimize and create all kinds of new spatial parallel manipulator with a desired dexterous workspace.

Multi-objective formulations are realistic models for many complex engineering optimization problems. In many real-life problems, objectives under consideration conflict with each other, and optimizing a particular solution with respect to a single objective can result in unacceptable results with respect to the other objectives. A reasonable solution to a multi-objective problem is to investigate a set of solutions, each of which satisfies the objectives at an acceptable level without being dominated by any other solution. In this paper, an overview and tutorial is presented describing genetic algorithms (GA) developed specifically for problems with multiple objectives. They differ primarily from traditional GA by using specialized fitness functions and introducing methods to promote solution diversity.

A compact, portable robot called CoBRASurge (Compact Bevel-geared Robot for Advanced Surgery) has been developed for tool guidance in minimally invasive surgery (MIS). It uses a spherical mechanism composed of bevel gears to achieve the necessary workspace in four degrees of freedom (DOF). Four DC motors drive the robot, with surgeon-in-the-loop control guided by an ergonomic joystick. The robot workspace has been validated experimentally, and motion trajectory experiments have shown robust and stable control. Use of the robot for camera guidance in porcine models is described. These experiments indicate superior functionality of the robot. Future work will involve integration of higher-function surgical tools with multiple CoBRASurge modules to create a complete, highly autonomous and portable MIS robot system for telesurgery.

The TETROBOT is an actuated robotic structure which may be
reassembled into many different configurations while still being
controlled by the same hardware and software architecture. The TETROBOT
system addresses the needs of application domains, such as space,
undersea, mining, and construction, where adaptation to unstructured and
changing environments and custom design for rapid implementation are
required

The task of optimizing a complex system presents at least two levels of problems for the system designer. First, a class of optimization algorithms must be chosen that is suitable for application to the system. Second, various parameters of the optimization algorithm need to be tuned for efficiency. A class of adaptive search procedures called genetic algorithms (GA) has been used to optimize a wide variety of complex systems. GA's are applied to the second level task of identifying efficient GA's for a set of numerical optimization problems. The results are validated on an image registration problem. GA's are shown to be effective for both levels of the systems optimization problem.