Research Papers

Position Analysis, Workspace, and Optimization of a 3-P̱PS Spatial Manipulator

[+] Author and Article Information
M. Ruggiu

Department of Mechanical Engineering, University of Cagliari, Cagliari 09123, Italyruggiu@dimeca.unica.it

J. Mech. Des 131(5), 051010 (Apr 15, 2009) (9 pages) doi:10.1115/1.3116257 History: Received June 09, 2008; Revised February 19, 2009; Published April 15, 2009

The present paper describes the analytical solution of position kinematics for a three degree-of-freedom parallel manipulator. It also provides a numeric example of workspace calculation and a procedure for its optimization. The manipulator consists of a base and a moving platform connected to the base by three identical legs; each leg is provided with a P̱PS chain, where P̱ designates an actuated prismatic pair, P stands for a passive prismatic pair, and S a spherical pair. The direct analysis yields a nonlinear system with eight solutions at the most. The inverse analysis is solved in three relevant cases: (i) the orientation of the moving platform is given, (ii) the position of a reference point of the moving platform is given, and (iii) two rotations (pointing) and one translation (focusing) are given. In the present paper it is proved that case (i) yields an inverse singularity condition of the mechanism; case (ii) provides a nonlinear system with four distinct solutions at the most; case (iii) allows the finding of some geometrical configurations of the actuated pairs for minimizing parasitic movements in the case of a pointing/focusing operation of the manipulator.

Copyright © 2009 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 11

Comparison between δs calculated by different βs: ● β=0, +β=π/4, and ◻ β=π/2

Grahic Jump Location
Figure 1

Geometry of the 3-P̱PS

Grahic Jump Location
Figure 2

Kinematic description of the manipulator

Grahic Jump Location
Figure 6

Position of the reference point of the moving platform

Grahic Jump Location
Figure 7

Motion of the reference point in the z=0 plane

Grahic Jump Location
Figure 8

Definition of β

Grahic Jump Location
Figure 9

Comparison between δmin and δ(β=π/3): ● δmin and +δ(β=π/3)

Grahic Jump Location
Figure 10

Occurrence of optimal β values

Grahic Jump Location
Figure 3

Inverse kinematic singularity: sequence of motion

Grahic Jump Location
Figure 4

Euler angles of the moving platform

Grahic Jump Location
Figure 5

ψ and ϑ pointing Euler angles



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In