Research Papers

A Motion Synthesis Approach to Solving Alt-Burmester Problem by Exploiting Fourier Descriptor Relationship Between Path and Orientation Data

[+] Author and Article Information
Shashank Sharma

Computer-Aided Design and
Innovation Laboratory,
Department of Mechanical Engineering,
Stony Brook University,
Stony Brook, NY 11794-2300
e-mail: shashank.sharma@stonybrook.edu

Anurag Purwar

Computer-Aided Design and
Innovation Laboratory,
Department of Mechanical Engineering,
Stony Brook University,
Stony Brook, NY 11794-2300
e-mail: anurag.purwar@stonybrook.edu

Q. Jeffrey Ge

Department of Mechanical Engineering,
Stony Brook University,
Stony Brook, NY 11794-2300
e-mail: qiaode.ge@stonybrook.edu

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received March 29, 2018; final manuscript received November 15, 2018; published online December 17, 2018. Assoc. Editor: Andrew P. Murray.

J. Mechanisms Robotics 11(1), 011016 (Dec 17, 2018) (8 pages) Paper No: JMR-18-1084; doi: 10.1115/1.4042054 History: Received March 29, 2018; Revised November 15, 2018

This paper presents a generalized framework to solve m-pose, n-path-points mixed synthesis problems, known as the Alt-Burmester problems, using a task-driven motion synthesis approach. We aim to unify the path and motion synthesis problems into an approximate mixed synthesis framework. Fourier descriptors are used to establish a closed-form relationship between the path and orientation data. This relationship is then exploited to formulate mixed synthesis problems into pure motion synthesis ones. We use an efficient algebraic fitting based motion synthesis algorithm to enable simultaneous type and dimensional synthesis of planar four-bar linkages.

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Grahic Jump Location
Fig. 1

An overview of our approach to the Alt-Burmester problems: (a) specify m-pose, n-path points, (b) a task curve is fit through the m + n path points using Fourier series, (c) use the harmonic content of the path data to find the missing orientations at the n-path points, and (d) finally, compute both type and dimensions of planar four-bar linkages

Grahic Jump Location
Fig. 2

Visualization of parameters describing a four-bar mechanism

Grahic Jump Location
Fig. 3

Example 1: known target mechanism

Grahic Jump Location
Fig. 4

Example 1: mechanism generated using mixed synthesis algorithm

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Fig. 5

Example 2: mixed synthesis with fully constrained MSP computation for three poses and five path points

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Fig. 6

Example 2: over-constrained motion synthesis for eight poses produces a poor solution

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Fig. 7

Example 3: under-constrained mixed synthesis for two poses and four path points using additional mixed constraint

Grahic Jump Location
Fig. 8

Example 4: under-constrained mixed synthesis for three poses and one path points using additional motion constraint



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