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Research Papers

Speeding Up Topology Optimization of Compliant Mechanisms With a Pseudorigid-Body Model

[+] Author and Article Information
Venkatasubramanian Kalpathy Venkiteswaran

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: kalpathyvenkiteswaran.1@osu.edu

Omer Anil Turkkan

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: turkkan.1@osu.edu

Hai-Jun Su

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: su.298@osu.edu

1Corresponding author.

Manuscript received November 9, 2016; final manuscript received January 25, 2017; published online May 2, 2017. Assoc. Editor: Xilun Ding.

J. Mechanisms Robotics 9(4), 041007 (May 02, 2017) (9 pages) Paper No: JMR-16-1348; doi: 10.1115/1.4035992 History: Received November 09, 2016; Revised January 25, 2017

This paper seeks to speed up the topology optimization using a pseudorigid-body (PRB) model, which allows the kinetostatic equations to be explicitly represented in the form of nonlinear algebraic equations. PRB models can not only accommodate large deformations but more importantly reduce the number of variables compared to beam theory or finite element methods. A symmetric 3R model is developed and used to represent the beams in a compliant mechanism. The design space is divided into rectangular segments, while kinematic and static equations are derived using kinematic loops. The use of the gradient and hessian of the system equations leads to a faster solution process. Integer variables are used for developing the adjacency matrix, which is optimized by a genetic algorithm. Dynamic penalty functions describe the general and case-specific constraints. The effectiveness of the approach is demonstrated with the examples of a displacement inverter and a crimping mechanism. The approach outlined here is also capable of estimating the stress in the mechanism which was validated by comparing against finite element analysis. Future implementations of this method will incorporate other pseudorigid-body models for various types of compliant elements and also try to develop multimaterial designs.

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Figures

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Fig. 1

Schematic of design process: (a) definition of design space, (b) conversion to grid of PRB models, (c) optimal topology, and (d) final mechanism in initial and deformed configurations

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Fig. 2

Symmetric 3R PRB model in undeflected and deformed positions for a beam of unit length

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Fig. 3

Design space divided into a m × n grid. The four possible connections from node Nm+2 are shown.

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Fig. 4

A node with three connections emanating from it

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Fig. 5

A parallelogram mechanism is shown with the kinematic vectors after PRB discretization. Due to kinematic constraints, Z4,Z5, and Z9 share a minimization variable.

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Fig. 6

A shape-morphing mechanism is shown. On the top, initial design is shown, and the deformed compliant mechanism is shown on the bottom.

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Fig. 7

Problem definition for the compliant inverter mechanism

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Fig. 8

Best topology for inverter mechanism

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Fig. 9

Design for inverter mechanism after possible simplification and shape optimization. The different line thicknesses represent beam widths.

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Fig. 10

Stress plots of inverter mechanism in its deformed state calculated using PRB (top) and FEA (bottom)

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Fig. 11

Problem definition for the compliant crimping mechanism

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Fig. 12

Best topology for crimping mechanism

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Fig. 13

Design for crimper mechanism after shape optimization. The different line thicknesses represent beam widths.

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Fig. 14

Stress plots of crimping mechanism in its deformed state calculated using PRB (top) and FEA (bottom)

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