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Theory Of Machines And Mechanisms

In this paper an extension of Generalized Differential Evolution for constrained multi-objective (Pareto-)optimization is proposed. The proposed extension adds a mechanism for maintaining extent and distribution of the obtained non-dominated solutions approximating a Pareto front. The proposed extension is tested with a set of five benchmark multi-objective test problems and results are numerically compared to known global Pareto fronts and to results obtained with the elitist Non-Dominated Sorting Genetic Algorithm and Generalized Differential Evolution. Results show that the extension improves extent and distribution of solutions of Generalized Differential Evolution.

An extension of Generalized Differential Evolution for multi-objective optimization with constraints

A serial-parallel hybrid machine tool is expected to integrate the respective features of pure serial/parallel mechanism. The traditional method of hybridization is to connect n (n ≥ 2) mechanisms bottom to head, in which at least one should be a parallel mechanism. One unique approach called Mechanism Hybridization is to embed one serial mechanism inside of a pure parallel mechanism, which greatly changes its overall performance. Based on this idea, an X-Y gantry system including a five-axis hybrid manipulator is developed, which is expected to be applied as the next generation of computer numerical control machine. The inverse kinematics and Jacobian matrix are derived. Since performance improvement is one of the most important factors that greatly affect the application potential of hybrid manipulators in different industry fields, to deeply investigate the comprehensive features, the local/global performance indexes of stiffness, dexterity, and manipulability are mathematically modeled and mapped. A discrete-boundary-searching method is developed to calculate and visualize the workspace. Pareto-based evolutionary multiobjective performance optimization is implemented to simultaneously improve the four indexes, and the representative nondominated solutions are listed. The proposed methodologies are generic and applicable for the design, modeling, and improvement of other parallel/hybrid robotic machine tools.

Performance Analysis, Mapping, and Multiobjective Optimization of a Hybrid Robotic Machine Tool

A new class of reconfigurable parallel kinematic machines

Parallel kinematic mechanisms (PKM) have received particular attention due to their higher stiffness, increased payload capacity, and agility, when compared to their serial counterparts. Despite these significant advantages, however, most PKM designs, typically, yield limited workspace, problematic singularities, and configuration-dependent stiffness. In response, mechanism redundancy has emerged as an effective tool to address these and other problems. In this paper, we present an in-depth discussion of past research on PKM redundancy. The methodical review of the pertinent literature, first, introduces the concept of redundancy based on the number of actuators and the number of degrees of freedom required to perform a task and, then, discusses the two main types of redundancy according to the mobility of the mechanism, i.e., kinematic and actuation redundancy. Subsequently, research on the design aspects of redundant PKMs, including the various criteria used for design optimization is detailed. Primary advantages of PKM redundancy include workspace enlargement, singularity elimination/ avoidance, and improved joint-torque distribution. In this paper, these advantages are discussed in contrast to the main challenges redundant mechanisms present, such as in motion planning and control, and calibration. Other issues of PKM redundancy, briefly, presented herein for completeness are fault-tolerance, reconfigurability, cable-driven and hyper-redundant PKMs.

A Review of Redundant Parallel Kinematic Mechanisms

Design and Kinematical Performance Analysis of a 3-RUS/RRR Redundantly Actuated Parallel Mechanism for Ankle Rehabilitation

A new family of reconfigurable parallel mechanisms with diamond kinematotropic chain

Dimensional synthesis is one of the most difficult issues in the field of parallel robots with actuation redundancy. To deal with the optimal design of a redundantly actuated parallel robot used for ankle rehabilitation, a methodology of dimensional synthesis based on multi-objective optimization is presented. First, the dimensional synthesis of the redundant parallel robot is formulated as a nonlinear constrained multi-objective optimization problem. Then four objective functions, separately reflecting occupied space, input/output transmission and torque performances, and multi-criteria constraints, such as dimension, interference and kinematics, are defined. In consideration of the passive exercise of plantar/dorsiflexion requiring large output moment, a torque index is proposed. To cope with the actuation redundancy of the parallel robot, a new output transmission index is defined as well. The multi-objective optimization problem is solved by using a modified Differential Evolution(DE) algorithm, which is characterized by new selection and mutation strategies. Meanwhile, a special penalty method is presented to tackle the multi-criteria constraints. Finally, numerical experiments for different optimization algorithms are implemented. The computation results show that the proposed indices of output transmission and torque, and constraint handling are effective for the redundant parallel robot; the modified DE algorithm is superior to the other tested algorithms, in terms of the ability of global search and the number of non-dominated solutions. The proposed methodology of multi-objective optimization can be also applied to the dimensional synthesis of other redundantly actuated parallel robots only with rotational movements.

Multi-objective optimization of a parallel ankle rehabilitation robot using modified differential evolution algorithm

In this paper, we present the design of two serial spherical mechanisms to substitute for a single spherical joint that is usually used to connect the platform with the base in three degrees of freedom parallel mechanisms. According to the principle derived from the conceptual design, through using the two serial spherical mechanisms as the constraint limb, several redundantly actuated parallel mechanisms are proposed for ankle rehabilitation. The proposed parallel mechanisms all can perform the rotational movements of the ankle in three directions while at the same time the mechanism center of rotations can match the ankle axes of rotations compared with other multi-degree-of-freedom devices, due to the structural characteristics of the special constraint limb and platform. Two special parallel mechanisms are selected to analyze their kinematical performances, such as workspace, dexterity, singularity, and stiffness, based on the computed Jacobian. The results show that the proposed scheme of actuator redundancy can guarantee that the redundantly actuated parallel mechanisms have no singularity, better dexterity, and stiffness within the prescribed workspace in comparison with the corresponding non-redundant parallel mechanisms. In addition, the proposed mechanisms possess certain reconfigurable capacity based on control strategies or rehabilitation modes to obtain sound performance for completing ankle rehabilitation exercise.

Design and kinematic analysis of redundantly actuated parallel mechanisms for ankle rehabilitation

This paper presents a novel reconfigurable parallel mechanism, which can serve as a machine tool. The proposed parallel mechanism can change its structure parameters by driving a bevel gear system fixed in the base platform. First, the forward and inverse kinematics of the proposed mechanism are investigated. Second, the reachable workspace and Jacobian matrix are conducted. Based on the Jacobian matrix, the stiffness model and dexterity of the end effector are developed in detail. Finally, a multi-objective optimization is performed by using the Genetic Algorithm, and the workspace and global performance indexes of stiffness as well as the dexterity are considered as the performance indices to improve the performance of the reconfigurable parallel mechanism. Finally, Pareto frontier figure and several tables are provided to illustrate the results of the optimization. The results showed the proposed method has improved the performance of the reconfigurable machine tool in terms of its stiffness and dexterity.

Sheng Guo

Papers

Design and Kinematical Performance Analysis of a 3-RUS/RRR Redundantly Actuated Parallel Mechanism for Ankle Rehabilitation

A new family of reconfigurable parallel mechanisms with diamond kinematotropic chain

Multi-objective optimization of a parallel ankle rehabilitation robot using modified differential evolution algorithm

Design and kinematic analysis of redundantly actuated parallel mechanisms for ankle rehabilitation

Kinematic analysis and multi-objective optimization of a new reconfigurable parallel mechanism with high stiffness