0
Research Papers

Wrench Accuracy for Parallel Manipulators and Interval Dependency

[+] Author and Article Information
Leila Notash

Department of Mechanical and
Materials Engineering,
Queen's University,
Kingston, ON K7L 3N6, Canada
e-mail: Leila.Notash@queensu.ca

Manuscript received July 11, 2016; final manuscript received November 1, 2016; published online December 2, 2016. Assoc. Editor: Raffaele Di Gregorio.

J. Mechanisms Robotics 9(1), 011008 (Dec 02, 2016) (9 pages) Paper No: JMR-16-1201; doi: 10.1115/1.4035221 History: Received July 11, 2016; Revised November 01, 2016

In this paper, the wrench accuracy for parallel manipulators is examined under variations in parameters and data. The solution sets of actuator forces/torques are investigated utilizing interval arithmetic (IA). Implementation issues of interval arithmetic to analyze the performance of manipulators are addressed, including the consideration of dependencies in parameters and the design of input vectors to generate the required wrench. Specifically, the effect of the dependency within and among the entries of the Jacobian matrix is studied, and methodologies for reducing and/or eliminating the overestimation of solution set are presented. In addition, the subset of solution set that produces platform wrenches within the required lower and upper bounds is modeled. Furthermore, the formulation of solutions that provide any platform wrench within the defined interval is examined. Intersection of these two sets, if any, results in the given interval platform wrench. Implementation of the methods to identify the solution for actuator forces/torques is presented on example parallel manipulators.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Planar parallel manipulators with (a) two actuators and (b) three actuators

Grahic Jump Location
Fig. 2

Parameters of 2DOF parallel manipulators

Grahic Jump Location
Fig. 3

Solution sets of Example 1: (a) solution using six parameters and (b) and (c) lines that characterize tolerance solution

Grahic Jump Location
Fig. 4

Solution sets of Example 1 using optimum bounds of Jacobian matrix: (a) solution using six parameters and (b) and (c) tolerance solution using closed half-planes

Grahic Jump Location
Fig. 5

Solution sets of Example 1: (a) with ai and p as independent parameters, (b) three solution sets, and (c) tolerance solution using 256 lines and its vertices

Grahic Jump Location
Fig. 6

Solution sets of Example 2: (a) tolerance and control solutions using 16 lines and discrete method, (b) zoomed-in tolerance solution using closed half-planes, and (c) control solution using closed half-planes in each quadrant

Grahic Jump Location
Fig. 7

Solution sets of Example 3: (a) solution and (b) control solution using discrete method and intersections of closed half-planes

Tables

Errata

Discussions

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