Dimensional optimization of 6-DOF 3-CCC type asymmetric parallel manipulator

Abstract

In this paper, dimensional optimization of a six-degrees-of-freedom (DOF) 3-CCC (C: cylindrical joint) type asymmetric parallel manipulator (APM) is performed by using particle swarm optimization (PSO). The 3-CCC APM constructed by defining three angle and three distance constraints between base and moving platforms is a member of 3D3A generalized Stewart-Gough platform (GSP) type parallel manipulators. The dimensional optimization purposes to find the optimum limb lengths, lengths of line segments on the base and moving platforms, attachment points of the line segments on the base platform, the orientation angles of the moving platform, and position of the end-effector in the reachable workspace in order to maximize the translational and orientational dexterous workspaces of the 3-CCC APM, separately. The dexterous workspaces are obtained by applying condition number and minimum singular values of the Jacobian matrix. The optimization results are compared with the traditional GSP manipulator for illustrating the kinematic performance of 3-CCC APM. Optimizations show that 3-CCC APM have superior dexterous workspace characteristics than the traditional GSP manipulator.

Parallel manipulator software tool for design, analysis, and simulation of 195 GSP mechanisms

“…Dexterity is one of the most important kinematic metrics used for parallel manipulators. It can be described as the capability of performing small displacement in any directions as easily as possible . Dexterity based on the condition number of the Jacobian matrix is described as where and are the minimum and maximum singular values of the Jacobian matrix, respectively.…”

“…It should be noted that illustrates the singular configuration while demonstrates the best configuration where the end‐effector exerts equal forces on any direction. Minimum singular values of the Jacobian matrix are also an important criterion that can be used for restricting motion of end‐effector at a minimum allowable speed .…”

Development of derivation of inverse Jacobian matrices for 195 6-DOF GSP mechanisms

“…The end points of the line segments are located on the circumferential circle of a hexagon whose corner points are labeled as A 1 A 2 , · · · ,A 5 , and A 6 . The moving platform of the mechanism is constructed by using the 6 points located on the circumferential circle of a hexagon and whose corner points were labeled as B 1 B 2 , · · · ,B 5 , and B 6 The base and moving platforms were connected to each other by using the 6 CPS type legs whose active prismatic joints were labeled as d 1 d 2 , · · · ,d 5 , and d 6 . Since the mechanism is symmetrical, the 6 × 6 inverse Jacobian matrix of this mechanism is produced by using the row vector given in Eq.…”

“…They solved the forward kinematics and the Jacobian matrix of the new 3CCC mechanism. Toz and Kucuk [5] performed the dimensional optimization of the mechanism proposed by Gan et al [3,4] and showed that the mechanism has better dexterous workspace characteristics than the traditional GSP manipulator. Luo et al [6,7] proposed a new method for solving the forward kinematics of 4SPS-2CCS and 5SPS-1CCS mechanisms using quaternions, where S and P denote spherical and prismatic joints, respectively.…”

“…Subsequently, the inverse Jacobian matrices of the 195 6-DOF GSP mechanisms were symbolically derived. It is well known that the inverse Jacobian matrix provides an instantaneous transformation between joint velocities and linear and angular velocities of the end-effector [5]. It can be used in several analysis processes of these mechanisms, such as the performance evaluation [9][10][11][12][13][14] and dynamical analysis [15].…”