Direct Singular Positions of 3RPS Parallel Manipulators

Abstract

In this study a procedure to obtain direct singular positions of a 3RPS parallel manipulator is presented. If the heights of 3 spherical joints, denoted by d1n, d2n, and d3n respectively, are used as coordinate axes, then the workspace of the moving platform may be represented as an inclined solid cylinder in this coordinate system. The location of a point on the solid circular cylinder determines a configuration of the manipulator’s moving platform. The procedure to locate direct singular positions consists of two steps, the orientation of the moving platform is assumed first, from which the horizontal position of the moving platform may be obtained; then in the second step the heights that make determinant of Jacobian matrix vanish may always be determined. Results show that unless the moving platform is normal to the base, in which case there exist only one or two singular configurations, otherwise there are always three singular configurations corresponding to a moving platform’s orientation.

Kinematic Analysis of a 3-Axis Parallel Manipulator: The P3

“…For example, Z3 head in machine tool [4], telescope application [5], motion simulator [6], micromanipulator [7], and coordinate measuring machine [8]. Much progress regarding kinematics analysis [9][10][11][12], dimensional synthesis [13][14][15][16][17], singularity [18,19], dynamics [12,20,21], and parasitic motion [22] has been obtained. Particularly, a new 1T2R PM with motion bifurcation of the end tool proposed for machine tool application [23].…”

Optimal dimensional synthesis of force feedback lower arm exoskeletons

“…The 3RPS platform, first introduced by Lee et al [21], and further analyzed in [22], consists of five bodies: a base platform F , three extensible links R, S, T , and a moving platform W . The end-effector held by the operator is rigidly attached to the moving platform W .…”

Analyses of Inverse Kinematics, Statics and Workspace of a Novel 3RPS- 3SPR Serial-Parallel Manipulator

“…The improved 2(3SPR) S-PM with compact topology can effectively diminish undesirable deflections and the presence of bending moments over *Address correspondence to this author at the Robotics Research Center, College of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei Qinhuangdao, China; Tel: 8613230307616; Fax: 86-335-8074783; E-mail: hbz0001@yahoo.com.cn the kinematical pairs which affecting the accuracy of this manipulator [11]. From this point of view, a novel S-PM which consists of a 3RPS PM [16][17][18] and its invertible structure 3SPR PM [19] adopting compact topology by using compound spherical joint [20] is investigated in this paper.…”