Research Papers: Mechanisms and Robotics

Kinematic Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms

[+] Author and Article Information
Andrew P. Murray

Mechanical and Aerospace Engineering, University of Dayton, Dayton, OH 45469murray@udayton.edu

James P. Schmiedeler

Mechanical Engineering, The Ohio State University, Columbus, OH 43210schmiedeler.2@osu.edu

Brian M. Korte

Mechanical Engineering, The Ohio State University, Columbus, OH 43210korte.16@osu.edu

J. Mech. Des 130(3), 032302 (Feb 04, 2008) (10 pages) doi:10.1115/1.2829892 History: Received July 21, 2006; Revised July 13, 2007; Published February 04, 2008

This paper presents a kinematic procedure to synthesize planar mechanisms, composed of rigid links and revolute joints, capable of approximating a shape change defined by a set of curves. These “morphing curves”, referred to as design profiles, differ from each other by a combination of rigid-body displacement and shape change. Design profiles are converted to piecewise linear curves, referred to as target profiles, that can be readily manipulated. In the segmentation phase, the geometry of rigid links that approximate the shapes of corresponding segments from each target profile is determined. In the mechanization phase, these rigid links are joined together at their end points with revolute joints to form a single chain. Dyads are then added to reduce the number of degrees of freedom (DOF’s) to any desired value, typically 1. The approach can be applied to any number of design profiles that can be approximated with any number of rigid links, which can then be used to construct a mechanism with any number of DOF’s. Naturally, greater difficulty is encountered for larger numbers of design profiles and/or links and for more dramatic changes in shape. The procedure is demonstrated with examples of single-DOF mechanisms approximating shape changes between two and three design profiles.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

(a) Design profiles that define a shape change. (b) Chain of four rigid segments jointed together shown relative to each design profile. (c) Solution single-DOF mechanism synthesized from the chain.

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Figure 2

Two design profiles (solid lines) and their target profiles (dashed lines). The top three-point design profile labeled (a,b) is represented by a five-point target profile labeled (x,y). The five-point, unlabeled bottom design profile has the same arclength as the top design profile, but the two five-point target profiles have different arclengths.

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Figure 3

(a) Three target profiles. (b) Two of the target profiles are shifted to minimize D relative to the third. (c) A mean profile (solid line). (d) The mean profile shifted to minimize D relative to each of the original target profiles.

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Figure 4

Portions of two rigid segments (solid light gray and black lines) shown at top in their individual distance-minimizing positions relative to a portion of a target profile (dashed medium gray lines) and at bottom assembled together as a chain with a revolute at their end points. This is a portion of target profile 1 and the solution segments from the example in Sec. 5 (shown in a different orientation). The error for the two segments in combination increases slightly after they are assembled, primarily because of the displacement of the left segment (light gray).

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Figure 5

(a) Proximity to singularity of the four-bar sublinkage of the example in Sec. 5. The maximum transmission angle is shown with solid lines, and the minimum with dashed. (b) Singular configurations between design positions with a candidate circle/center-point pair for additional rigid segment.

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Figure 6

Single-DOF mechanism changing between three design profiles

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Figure 7

Single-DOF mechanism changing from “U” to “D”




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