Research Papers

Homotopy Directed Optimization to Design a Six-Bar Linkage for a Lower Limb With a Natural Ankle Trajectory

[+] Author and Article Information
Brandon Y. Tsuge

Mechanical and Aerospace Engineering,
University of California,
Irvine, CA 92697
e-mail: btsuge@uci.edu

Mark M. Plecnik

Electrical Engineering and Computer Science,
University of California,
Berkeley, CA 94720
e-mail: mplecnik@berkeley.edu

J. Michael McCarthy

Fellow ASME
Robotics and Automation Laboratory,
Department of Mechanical and
Aerospace Engineering,
University of California,
Irvine, CA 92697
e-mail: jmmccart@uci.edu

Manuscript received August 15, 2015; final manuscript received July 3, 2016; published online September 8, 2016. Assoc. Editor: Qiaode Jeffrey Ge.

J. Mechanisms Robotics 8(6), 061009 (Sep 08, 2016) (7 pages) Paper No: JMR-15-1225; doi: 10.1115/1.4034141 History: Received August 15, 2015; Revised July 03, 2016

This paper presents a synthesis method for the Stephenson III six-bar linkage that combines the direct solution of the synthesis equations with an optimization strategy to achieve increased performance for path generation. The path synthesis equations for a six-bar linkage can reach as many as 15 points on a curve; however, the degree of the polynomial system is 1046. In order to increase the number of accuracy points and decrease the complexity of the synthesis equations, a new formulation is used that combines 11 point synthesis with optimization techniques to obtain a six-bar linkage that minimizes the distance to 60 accuracy points. This homotopy directed optimization technique is demonstrated by obtaining a Stephenson III six-bar linkage that achieves a specified gait trajectory.

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Fig. 1

The ankle trajectories achieved by the ARTHuR Step Robot, Ref. [1]

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Fig. 2

Coordinates of the ankle during multiple gait cycles

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Fig. 3

Stephenson III six-bar linkage

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Fig. 4

Coordinates of the ankle relative to the hip joint

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Fig. 5

Ankle trajectory of a single gait cycle relative to the hip joint

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Fig. 6

Set of 60 precision points derived from a basis spline

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Fig. 7

Plot of the 11 starting precision points for the exact six-bar synthesis problem

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Fig. 8

One of 2003 linkage designs in the initial population positioned at the first precision point

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Fig. 9

Optimized Stephenson III linkage solutions that have the largest variance from each other

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Fig. 10

One of six optimized linkage solutions in a position with a slightly hyperextended knee joint

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Fig. 11

Solidworks model of the optimized linkage solution



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