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Position, Jacobian and workspace analysis of a 3-PSP spatial parallel manipulator

Authors
Journal
Robotics and Computer-Integrated Manufacturing
0736-5845
Publisher
Elsevier
Volume
29
Issue
4
Identifiers
DOI: 10.1016/j.rcim.2012.11.009
Keywords
  • Spatial Parallel Manipulator
  • Kinematics
  • Jacobian Analysis
  • Singularity
  • Workspace
Disciplines
  • Mathematics

Abstract

Abstract This paper investigates the problems of kinematics, Jacobian, singularity and workspace analysis of a spatial type of 3-PSP parallel manipulator. First, structure and motion variables of the robot are addressed. Two operational modes, non-pure translational and coupled mixed-type are considered. Two inverse kinematics solutions, an analytical and a numerical, for the two operational modes are presented. The direct kinematics of the robot is also solved utilizing a new geometrical approach. It is shown, unlike most parallel robots, the direct kinematics problem of this robot has a unique solution. Next, analytical expressions for the velocity and acceleration relations are derived in invariant form. Auxiliary vectors are introduced to eliminate passive velocity and acceleration vectors. The three types of conventional singularities are analyzed. The notion of non-pure rotational and non-pure translational Jacobian matrices is introduced. The non-pure rotational and non-pure translational Jacobian matrices are combined to form the Jacobian of constraint matrix which is then used to obtain the constraint singularity. Finally, two methods, a discretization method and one based on direct kinematics are presented and robot non-pure translation and coupled mixed-type reachable workspaces are obtained. The influence of tool length on workspace is also studied.

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