Synthesis of Path Generating Compliant Mechanisms Using Initially Curved Frame Elements

[+] Author and Article Information
Ashok Kumar Rai, Anupam Saxena

 Indian Institute of Technology, Kanpur, Kanpur 208 016, India

Nilesh D. Mankame

 General Motors Research & Development, Warren, MI 48090

J. Mech. Des 129(10), 1056-1063 (Oct 27, 2006) (8 pages) doi:10.1115/1.2757191 History: Received September 26, 2006; Revised October 27, 2006

Initially curved frame elements are used in this paper within an optimization-based framework for the systematic synthesis of compliant mechanisms (CMs) that can trace nonlinear paths. These elements exhibit a significantly wider range of mechanical responses to applied loads than the initially straight frame elements, which have been widely used in the past for the synthesis of CMs. As a consequence, fewer elements are required in the design discretization to obtain a CM with a desired mechanical response. The initial slopes at the two nodes of each element are treated as design variables that influence not only the shape of the members in a CM, but also the mechanical response of the latter. Building on our prior work, the proposed synthesis approach uses genetic algorithms with both binary (i.e., 0/1) and continuous design variables in conjunction with a co-rotational total Lagrangian finite element formulation and a Fourier shape descriptors-based objective function. This objective function is chosen for its ability to provide a robust comparison between the actual path traced by a candidate CM design and the desired path. Two synthesis examples are presented to demonstrate the synthesis procedure. The resulting designs are fabricated as is, without any postprocessing, and tested. The fabricated prototypes show good agreement with the design intent.

Copyright © 2007 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 9

Example 1: (a) Optimal solution shown in an intermediate displaced position with response output path (dark/black) and specified output path (light/green) and (b) magnified figure comparing the obtained (top/thick/blue) and desired (bottom/thin/red) paths

Grahic Jump Location
Figure 10

Example 1: Four deformed configurations of a polycarbonate prototype tracing the desired path

Grahic Jump Location
Figure 11

Example 3: (a) Optimal solution at an intermediate position with actual output path (dark, black) and specified output path (light, green) and (b) comparison of the obtained (upper, blue) and desired (lower, red) paths

Grahic Jump Location
Figure 12

Example 2: Three deformed configurations of a polycarbonate prototype tracing the desired path

Grahic Jump Location
Figure 8

Schematic of the problem specification for example 1

Grahic Jump Location
Figure 7

Intersection check: Hermite Bezier curves with coordinate boxes in the determination of intersection

Grahic Jump Location
Figure 6

Plots of different errors in shapes and sizes of the curves shown in Fig. 5

Grahic Jump Location
Figure 5

Different curves used to illustrate the performance of the individual error terms in the objective in Eq. 1

Grahic Jump Location
Figure 4

A grid of frame elements representing the initial design domain and reflecting node movement. The shapes of the curved frame elements change as design iterations progress.

Grahic Jump Location
Figure 3

Slopes (ω1,ω2) at the two ends of an element in its undeformed configuration are used as the shape design variables for that element

Grahic Jump Location
Figure 2

The characteristic deflection domains for an initially straight (a) and for an initially semicircular cantilever (b) subjected to end loads (from Mettlach (28))

Grahic Jump Location
Figure 1

Schematic representation of the problem




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