A Polynomial Homotopy Formulation of the Inverse Static Analysis of Planar Compliant Mechanisms

[+] Author and Article Information
Hai-Jun Su1

Virtual Reality Application Center, 1620 Howe Hall, Iowa State University, Ames, IA 50011haijunsu@iastate.edu

J. Michael McCarthy

Robotics and Automation Laboratory, University of California, Irvine, Irvine, CA 92697jmmccart@uci.edu


Address all correspondence to this author.

J. Mech. Des 128(4), 776-786 (Oct 04, 2005) (11 pages) doi:10.1115/1.2202137 History: Received June 07, 2005; Revised October 04, 2005

This paper formulates the inverse static analysis of planar compliant mechanisms in polynomial form. The goal is to find the equilibrium configurations of the system in response to a known force/moment applied to the mechanism. The geometric constraint of the linkage defines a set of kinematics equations which are combined with equilibrium equations obtained from partial derivatives of the potential-energy function. In order to apply polynomial homotopy solver to these equations, we approximate the linear torsion spring torque at each joint by using sine and cosine functions. The results obtained from the homotopy solver are then refined using Newton-Raphson iteration. To demonstrate the analysis steps, we study two example planar compliant mechanisms, a four-bar linkage with two torsional springs, and a parallel platform supported by three linear springs. Numerical examples are provided together with plots of the potential energy during a movement between selected equilibrium positions.

Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 4

A compliant four-bar linkage

Grahic Jump Location
Figure 5

A compliant platform mechanism with three flexible limbs

Grahic Jump Location
Figure 6

Six equilibrium configurations of a compliant four-bar linkage. Configuarations (a), (b), (c), and (d) are on one assembly, while (e) and (f) are on the other assembly.

Grahic Jump Location
Figure 7

Energy curve and its derivative for the compliant four-bar linkage

Grahic Jump Location
Figure 8

Four equilibrium configurations of an equilateral compliant platform

Grahic Jump Location
Figure 9

Potential energy and moment required to move between the four equilibrium configurations of the compliant platform

Grahic Jump Location
Figure 10

Six equilibrium configurations of the alternate form of the equilateral compliant platform

Grahic Jump Location
Figure 11

Potential energy and external loading required to move between the six configurations

Grahic Jump Location
Figure 12

The other 15 equilibrium configurations of the equilateral compliant mechanism

Grahic Jump Location
Figure 13

The other three equilibrium configurations of the alternative form of the equilateral compliant mechanism

Grahic Jump Location
Figure 1

A general three degree-of-freedom compliant platform mechanism and its rigid-body counterpart

Grahic Jump Location
Figure 2

Two typical flexural joints and their pseudo-rigid-body models

Grahic Jump Location
Figure 3

The linear function τ=kΔϕ and the approximating functions τ′(Δϕ). The maximum error is 1.5% for Δϕ∊[−π∕2,π∕2]




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