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
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Figure 1

Schematic representation of the problem

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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))

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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

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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.

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Figure 5

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

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Figure 6

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

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Figure 7

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

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Figure 8

Schematic of the problem specification for example 1

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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

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Figure 10

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

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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

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Figure 12

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



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