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Frontiers of Mechanical Engineering

Front. Mech. Eng.    2015, Vol. 10 Issue (1) : 7-19
A comprehensive analysis of a 3-P (Pa) S spatial parallel manipulator
Yuzhe LIU1,2,Liping WANG1,2,*(),Jun WU1,2,Jinsong WANG1,2
1. State Key Laboratory of Tribology and Institute of Manufacturing Engineering, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
2. Beijing Key Laboratory of Precision/Ultra-precision Manufacturing Equipments and Control, Beijing 100084, China
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In this paper, a novel 3-degree of freedom (3-DOF) spatial parallel kinematic machine (PKM) is analyzed. The manipulator owns three main motions (two rotations and one translation) and three concomitant motions (one rotation and two translations). At first, the structure of this spatial PKM is simplified according to the characteristic of each limb. Secondly, the kinematics model of this spatial PKM is set up. In addition, the relationship between the main motions and concomitant motions is studied. The workspaces respectively based on the outputs and inputs are derived and analyzed. Furthermore, the velocity model is put forward. Two indexes based on the velocity model are employed to investigate the performance of this spatial PKM. At last, the output error model can be obtained and simulated. The comprehensive kinematics analysis in this paper is greatly useful for the future applications of this spatial PKM.

Keywords parallel mechanism      concomitant motions      kinematics      workspaces      error model     
Corresponding Authors: Liping WANG   
Online First Date: 10 February 2015    Issue Date: 01 April 2015
 Cite this article:   
Yuzhe LIU,Liping WANG,Jun WU, et al. A comprehensive analysis of a 3-P (Pa) S spatial parallel manipulator[J]. Front. Mech. Eng., 2015, 10(1): 7-19.
Fig.1  The virtual prototype of a 3-P (Pa) S spatial parallel manipulator
Fig.2  Pa joint
Fig.3  Simplification of one limb
Fig.4  Kinematics model
Fig.5  T–T angle in 3-Dspace
Fig.6  T–T angle in the top view
Fig.7  The vector loop of each limb
a/mm b/mm l/mm
200 260 460
Tab.1  Structure parameters of the spatial parallel manipulator
Z/mm φ /(° ) θ /(° )
700 0-360 0-45
Tab.2  Ranges of the main motion parameters
Fig.8  Concomitant Motion of X direction
Fig.9  Concomitant Motion of Y direction
Fig.10  Workspace based on output
p1/mm p2/mm p3/mm
240-340 240-340 240-340
Tab.3  Ranges of the input parameters
Fig.11  Workspace based on input
Fig.12  Dexterity
Fig.13  Manipulability
Fig.14  Position error
Fig.15  Rotation error
Fig.16  Pose error
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