Methodologies for the optimal design of parallel manipulators

In this paper the problem of determining a manipulator design so that its workspace corresponds to a prescribed workspace is considered. Two different strategies, resulting in two different types of optimization problem are considered. The first strategy attempts to obtain a good overall approximation to the prescribed workspace and results in an unconstrained optimization problem. The second strategy entails designing a manipulator so that its workspace fully encloses the prescribed workspace and results in a constrained optimization problem. Two specific formulations of the constrained problem are proposed. The first constrained problem simply aims to fit the manipulator workspace as exactly as possible to the prescribed workspace, while still ensuring that the prescribed workspace is fully enclosed. The second constrained optimization formulation is used to design a manipulator, the workspace of which fully encloses the prescribed workspace, but which is also well‐conditioned throughout the workspace with respect to some performance measure. The particular manipulator used to illustrate and evaluate these formulations is a simple 2‐dof planar parallel manipulator, and the final formulation is also applied to a 3‐dof planar parallel manipulator. Although the manipulators studied here are simple, the objective of this study is to obtain a robust numerical methodology which can be extended to more practical and complex manipulators. Copyright © 2003 John Wiley & Sons, Ltd.     

Design, analysis and fabrication of a novel three degrees of freedom parallel robotic manipulator with decoupled motions

Most of the existing parallel robotic manipulators have coupled motion between the position and orientation of the end-effector. The complexity of the multi-axial manipulation produces the difficulty to control. This research deals with a lower mobility parallel manipulator with fully decoupled motions. The proposed parallel manipulator has three degrees of freedom and can be utilized for parts assembly and light machining tasks that require large workspace, high dexterity, high loading capacity, and considerable stiffness. The manipulator consists of a moving platform that is connected to a fixed base by three pairwise orthogonal legs which are comprised of one cylinder, one revolute and one universal joint respectively. The mobility of the manipulator and structure of the inactive joint are analyzed. Kinematics of the manipulator including inverse and forward kinematics, velocity equation, kinematic singularities, and stiffness are studied. The workspace of the parallel manipulator is examined. A design optimization is conducted with the prescribed workspace. It has been found that due to the special arrangement of the legs and joints, this parallel manipulator possesses fully isotropic. This advantage has great potential for machine tools and coordinate measuring machine. The experiment on the prototype verifies its feasibility as a portable parallel robotic machine tool.     

A numerical method for the determination of dextrous workspaces of Gough–Stewart platforms

An optimization approach to the computation of the boundaries of different dextrous workspaces of parallel manipulators is presented. A specific dextrous workspace is the region in space in which, at each position of the working point, a manipulator can control the orientation of its upper working platform through a specified range of orientation angles. Here the dextrous workspace is determined from the intersection of suitably chosen fixed orientation workspaces, which are found by application of a constrained optimization algorithm. The procedure is simple and has the considerable advantage that it may easily be automated. The method is illustrated by its application to both a planar and spatial Gough–Stewart platform. Copyright © 2001 John Wiley & Sons, Ltd.     

Optimization of a planar tendon-driven parallel manipulator for a maximal dextrous workspace

In this article, new methodologies for determining the tension distribution and optimal configurations of planar tendon-driven parallel manipulators (TDPMs) are presented. TDPMs are characterized by the use of cables in place of the linear actuators used in most parallel manipulators. Three separate, but inter-related topics are examined in this article, and methodologies for addressing them are proposed. The first is the determination of cable forces for overconstrained tendon-driven manipulators, which is necessary in order to address the second topic, namely, the development of a methodology for workspace determination of tendon-driven manipulators. The final topic examined is the dimensional synthesis of tendon-driven manipulators for a large dextrous workspace. The numerical methodologies developed here have potential for easy application to more complex spatial cases.     

Workspace-constrained optimal design of three-degrees-of-freedom parallel manipulators with minimum parasitic motions by integrating interval analysis,region mapping and differential evolution

Three-degrees-of-freedom (3-DOF) parallel manipulators have many advantages such as simple structure, fewer actuators, and lower maintenance cost. However, parasitic motions may degrade the positioning accuracy of the platforms. In order to design 3-DOF parallel manipulators which can fulfil specified workspace requirements and exhibit minimum parasitic motions, the design problem is formulated into a minimax problem with workspace constraints. Then, an interval-based method is exploited to determine the feasible solution set which is derived as a union of many scattered parameter intervals (boxes). Then, a new approach based on region mapping and a powerful optimizer (namely differential evolution) is proposed to solve the optimization problem over scattered search regions. Benchmark tests show the superiority of the proposed approach. Then, the approach and interval analysis are used to solve a real-world design problem involving a 3-DOF manipulator. Numerical results demonstrate the effectiveness and advantages of the proposed design method.     

Revolute manipulator workspace optimization using a modified bacteria foraging algorithm: A comparative study

Robotic manipulators with three-revolute (3R) motions to attain desired positional configurations are very common in industrial robots. The capability of these robots depends largely on the workspace of the manipulator in addition to other parameters. In this study, an evolutionary optimization algorithm based on the foraging behaviour of the Escherichia coli bacteria present in the human intestine is utilized to optimize the workspace volume of a 3R manipulator. The new optimization method is modified from the original algorithm for faster convergence. This method is also useful for optimization problems in a highly constrained environment, such as robot workspace optimization. The new approach for workspace optimization of 3R manipulators is tested using three cases. The test results are compared with standard results available using other optimization algorithms, i.e. the differential evolution algorithm, the genetic algorithm and the particle swarm optimization algorithm. The present method is found to be superior to the other methods in terms of computational efficiency.     

A mathematical optimization methodology for the optimal design of a planar robotic manipulator

A general optimization methodology for the optimal design of robotic manipulators is presented and illustrated by its application to a realistic and practical three‐link revolute‐joint planar manipulator. The end‐effector carries out a prescribed vertical motion for which, respectively, the average torque requirement from electrical driving motors, and the electric input energy to the driving motors are minimized with respect to positional and dimensional design variables. In addition to simple physical bounds placed on the variables, the maximum deliverable torques of the driving motors and the allowable joint angles between successive links represent further constraints on the system. The optimization is carried out via a penalty function formulation of the constrained problem to which a proven robust unconstrained optimization method is applied. The problem of singularities (also known as degeneracy or lock‐up), which may occur for certain choices of design variables, is successfully dealt with by means of a specially proposed procedure in which a high artificial objective function value is computed for such ‘lock‐up trajectories’. Designs are obtained that are feasible and practical with reductions in the objective functions in comparison to that of arbitrarily chosen infeasible initial designs. Copyright © 1999 John Wiley & Sons, Ltd.     

基于改进目标检测算法的AGV避障方法研究

目的 针对食品包装的抓取和装配,利用人工成本高且容易装错等问题,基于方位特征(POC)方程的并联机构结构综合方法,提出一种以3PUPaR并联机构为主体的抓取机器人机构。方法 计算3PUPaR并联机构的自由度、方位特征集以及耦合度等拓扑特性,验证机构具有空间纯移动的运动特性,建立机构的运动学逆解方程,基于此,采用数值法得到机构的工作空间与运动灵巧度。并研究参数尺寸大小对工作空间与全局灵巧度的影响,以全局灵巧度和工作空间为优化目标,选择具有Pareto解的NSGA-II算法完成多目标参数优化。结果 结果表明,机构具有较大且连续的工作空间。结论 该新型三自由度并联机器人能够满足食品包装的抓取和装配时运动范围。     

Design optimization of a spatial hybrid mechanism for micromanipulation

Traditional parallel manipulators suffer from errors due to backlash, hysteresis, and vibration in the mechanical joints. The hybrid mechanism is built through the reconfiguration of parallel-serial structure. In this paper, a new 3SPS + RPR spatial hybrid mechanism which has three degrees of freedom (DOF) and can generate motions in a microscopic scale is proposed. As a reliable compliant hybrid mechanism which provides micro/nano scale micromotion with high accuracy, it can be utilized for biomedical engineering and fiber optics industry. The detailed design of the structure is first introduced, followed by the kinematic analysis and performance evaluation. Based on the kinetostatic model, the joint and link compliances of the passive constraining leg are investigated. Second, a finite-element analysis of resultant stress, strain, and deformations is evaluated based upon different inputs of the three piezoelectric actuators. Finally, the genetic algorithms and radial basis function networks are implemented to search for the optimal architecture and behavior parameters in terms of global stiffness/compliance, dexterity and manipulability. The proposed analysis and optimization methodology is intuitive and effective that offers a constructive way for design optimization of the family of parallel/hybrid manipulators.     

Multi-objective optimization of stiffness and workspace for a parallel kinematic machine

This paper presents optimizations of a parallel kinematic manipulator used for a machine tool in terms of its workspace and stiffness. The system stiffness and workspace of the parallel manipulator are conducted in the paper. In order to locate the maximum system stiffness and workspace, single and multi-objective optimizations are performed in terms of rotation angles in x and y axes and translation displacement in z axis with genetic algorithms. By optimizing the design variables including geometric dimensions of the manipulator, the system stiffness and workspace of the proposed parallel kinematic manipulator has been greatly improved.     

新型四自由度3T1R并联机器人机构运动学分析与优化设计

目的 针对自动化生产线分拣需求,提出一种新型四自由度的三平移一转动（3T1R）并联机器人机构。方法 根据方位特征集设计理论验证并联机器人机构的运动性质。利用机构的构型特点建立运动学方程模型,对其进行位置正解和逆解的分析,通过数值法搜索得到并联机器人机构的工作空间图形和转动能力等高线图。同时分析并联机器人机构的雅可比矩阵JX以及奇异性。最后以工作空间最大化作为适应度函数,基于遗传算法对机构结构尺寸进行最优化分析。结果 该机构操作空间具有规则形状、无空洞、较大的特点,优化后的并联机器人机构工作空间性能提升45%。结论 操作空间内运动灵活性较好,优化后工作空间性能得到显著改善。在电子包装自动化生产线搬运分拣领域具有较好的应用前景。     

Minimum time collision-free path planning for robotic assembly

Optimum path planning of manipulator arms in assembly applications involves the selection of the optimum combination of the robot control variables under the constraints imposed by the robot's physical capabilities and the condition of the working area. The present paper describes an approach based on numerical optimization techniques to plan collision-free paths, and on Taguchi parameter design methodology to optimize the control parameters of the pick-and-place operation that would yield minimum cycle time     

A general approach for optimal kinematic design of 6-DOF parallel manipulators

Optimal kinematic design of parallel manipulators is a challenging problem. In this work, an attempt has been made to present a generalized approach of kinematic design for a 6-legged parallel manipulator, by considering only the minimally required design parameters. The same approach has been used to design a 7-legged redundant parallel manipulator. Two ways of introducing redundancy into the parallel manipulator have been demonstrated and comparison between them has been presented.     

Synthesis of a spatial 3-RPS parallel manipulator based on physical constraints

The range of motion of the moving platform of a spatial 3-RPS parallel manipulator will be greatly influenced by the physical constraints such as limits on the lengths of the limbs and the range of motion of the spherical joints. Therefore, while synthesizing the parallel manipulator, the physical constraints have to be considered. Synthesis of the manipulator involves determination of the architectural parameters of the manipulator so that a point on the moving platform passes through a prescribed set of positions in space. This paper presents a synthesis procedure that determines location and direction of revolute joints and location of spherical joints along with orientation of sockets of spherical joints, considering the physical constraints. The synthesis procedure is demonstrated through a numerical example.     

新型3T1R并联机器人机构运动学分析与参数优化

目的 针对生产线码垛作业货物搬运需求,设计一种3T1R码垛并联机器人机构.方法 利用方位特征方程分析机器人机构的自由度、耦合度、方位特征集等拓扑结构特性.根据运动副的构型建立运动学逆解模型,考虑到码垛机器人运动范围的精度需求,采用一种新型的数值搜索法实现并联机构工作空间的快速高效搜索,同时,分析结构参数对工作空间体积的影响,选择鲸鱼优化算法对结构参数进行最优化设计.结果 分析得到的机构工作空间较大且连续性较好,新型的数值搜索法可快速有效地搜索,得到准确的工作空间边界.结论 优化后的并联机构具有良好的工作空间和较好的应用前景.     

机器人操作臂可达能力研究

为了评价机器人操作臂跟踪目标的能力,导出了操作臂可达函数的表达式,定义了操作臂的可达能力,研究了操作臂自由度数、关节转角约束、关节连杆长度对可达能力的影响,建立了操作臂可达目标的存在条件。最后,以过定点、固定位姿和连续轨迹目标为例,说明了操作臂可达能力对操作的重要性,也为操作臂的设计提供了理论依据。     

Extreme reaches and maximal reachable workspace for rotary tools mounted on a Stewart platform manipulator

Abstract

A new type of problem associated with the extreme reaches of the Stewart platform manipulator is dealt with in this paper. Given a specified orientation of the tool axis, the problem involves finding the extreme distance that the tool bit mounted on the mobile platform can reach from its home position along any specified direction. During the motion, the mobile platform is allowed to be rotated about the tool axis to adjust the configuration of the driving mechanism to prevent premature activation of the kinematic constraints. A numerical optimization algorithm based on the concept of the cyclic coordinate descent method is developed for solving this problem, in which all three types of kinematic constraints, namely the actuator stroke constraint, the passive joint limitations, and the link interference conditions, have been taken into account. In addition, a numerical example is presented to demonstrate the ability of the proposed method to find the optimal reachable workspace of the robot.     

基于2-CPR/UPS三平移并联机构的移印机运动学分析

目的提出一种基于2-CPR/UPS并联机构的三平移移印机,以扩展并联机构的应用领域,提高移印印刷质量。方法应用螺旋理论求解机构的自由度,并用修正的Kutzbach-Grübler公式进行验证。建立该机构Jacobian矩阵的数学模型,运用极限坐标搜索法求解其工作空间。根据Jacobian矩阵对机构奇异性进行分析,获得灵巧度指标在工作空间中的分布规律。结果该机构可实现三平移运动,工作空间呈长方体形状,内部连续无空洞且无奇异位置,灵巧度指标在工作空间中分布均匀。结论该三平移移印机可满足移印时的运动及工作范围需求,研究结果表明该机构在工作空间中无奇异位置且灵巧度性能良好。     

Tailoring materials with prescribed elastic properties

This paper describes a method to design the periodic microstructure of a material to obtain prescribed constitutive properties. The microstructure is modelled as a truss or thin frame structure in 2 and 3 dimensions. The problem of finding the simplest possible microstructure with the prescribed elastic properties can be called an inverse homogenization problem, and is formulated as an optimization problem of finding a microstructure with the lowest possible weight which fulfils the specified behavioral requirements. A full ground structure known from topology optimization of trusses is used as starting guess for the optimization algorithm. This implies that the optimal microstructure of a base cell is found from a truss or frame structure with 120 possible members in the 2-dimensional case and 2016 possible members in the 3-dimensional case. The material parameters are found by a numerical homogenization method, using Finite-Elements to model the representative base cell, and the optimization problem is solved by an optimality criteria method.

Numerical examples in two and three dimensions show that it is possible to design materials with many different properties using base cells modelled as truss or frame works. Hereunder is shown that it is possible to tailor extreme materials, such as isotropic materials with Poisson's ratio close to − 1, 0 and 0.5, by the proposed method. Some of the proposed materials have been tested as macro models which demonstrate the expected behaviour.     

A novel six degrees-of-freedom parallel manipulator for aircraft fuselage assemble and its trajectory planning

Parallel manipulators have been successfully used for pose adjustment. However, aircraft fuselages are heavy and have complex shapes, so the existing parallel manipulators are not suitable for aircraft fuselages. For the first time, this paper presents a novel six degrees of freedom parallel manipulator for aircraft fuselages. Compared with other parallel manipulators, the presented parallel manipulator is suitable for large round parts. The Jacobi matrix of the presented parallel manipulator is derived, which is expressed by roll, pitch, and yaw. Using the derived Jacobi matrix, inverse kinematics of the presented parallel manipulator is investigated systemically. Combining Newton’s second law with Euler equations, dynamic equations of the manipulator are derived. Using the derived dynamic equations, inverse dynamics of the manipulator are also investigated systemically. For improving safety and efficiency of fuselage pose adjustment, a new trajectory planning algorithm is proposed which is based on the minimum mean force. Simulation experiment results demonstrated the ability of the trajectory planning algorithm to achieve stable movement comparable to the time-optimal trajectory planning algorithm. At the conclusion of this paper, practical applications of the presented parallel manipulator are shown.