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Research Papers

# A New Method to Calculate the Force and Moment Workspaces of Actuation Redundant Spatial Parallel Manipulators

[+] Author and Article Information
Venus Garg

Department of Mechanical Engineering, University of New Brunswick, Fredericton, NB, E3B 5A3, Canadavenus.garg@unb.ca

Juan A. Carretero1

Department of Mechanical Engineering, University of New Brunswick, Fredericton, NB, E3B 5A3, Canadajuan.carretero@unb.ca

Scott B. Nokleby

Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, Oshawa, ON, L1H 7K4, Canadascott.nokleby@uoit.ca

Angles $α$, $β$, and $γ$ must satisfy $cos2 α+cos2 β cos2 γ=1$. That is, only two of the three angles need to be specified.

Note that, for symmetrical actuators, $τmax=−τmin$. Without any loss of generality this will be the case assumed throughout the rest of this work.

The term maxed-out actuator is used to identify an actuator at one of its two extreme torque limits.

1

Corresponding author.

J. Mechanisms Robotics 1(3), 031004 (Jul 14, 2009) (8 pages) doi:10.1115/1.3147184 History: Received June 04, 2008; Revised December 12, 2008; Published July 14, 2009

## Abstract

A new method for obtaining the force and moment workspaces of spatial parallel manipulators (PMs) is presented. Force and moment workspaces are regions within which a manipulator can sustain/apply at least a certain value of force or moment in all directions. Here, the force and moment workspaces are found using a method, which explicitly sets the largest possible number of actuators to their maximum limits ensuring that the manipulator is performing at its best possible wrench capabilities. Two cases for obtaining these workspaces are used. The first gives the applicable/sustainable force with a prescribed moment whereas the second one gives the applicable/sustainable moment with a prescribed force. For illustration purposes, the method is applied to a six-degree-of-freedom (DOF) redundantly-actuated spatial PM, the $3-RRṞS$. The results are represented graphically as the boundaries of the workspace in the three-dimensional Cartesian space. These workspaces can be used as a powerful tool for path/task planning and PM design.

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Topics: Force , Manipulators

## Figures

Figure 1

Vector diagram for branch 1 of the 3-RRRS manipulator

Figure 2

Frame assignment of one branch of the 3-RRRS manipulator

Figure 3

Constant orientation workspace of the 3-RRṞS

Figure 4

Min-max force capabilities

Figure 5

Min-max moment capabilities

Figure 6

(a) Min-max force trend and(b) min-max moment for a direction from the origin toward the boundary of the orientation workspace for the force and moment cases, respectively. Bracket values represent radial limit (r[m]) of the workspace at the corresponding direction angle about the z axis.

Figure 7

Force workspaces

Figure 8

Moment workspaces

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