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Research Papers

Synthesis of Planar Mechanisms for Pick and Place Tasks With Guiding Positions

[+] Author and Article Information
Pierre Larochelle

Department of Mechanical and
Aerospace Engineering,
Robotics and Spatial Systems Laboratory,
Florida Institute of Technology,
Melbourne, FL 32901
e-mail: pierrel@fit.edu

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received November 7, 2013; final manuscript received September 6, 2014; published online December 4, 2014. Assoc. Editor: J.M. Selig.

J. Mechanisms Robotics 7(3), 031009 (Aug 01, 2015) (10 pages) Paper No: JMR-13-1227; doi: 10.1115/1.4028638 History: Received November 07, 2013; Revised September 06, 2014; Online December 04, 2014

A novel dimensional synthesis technique for solving the mixed exact and approximate motion synthesis problem for planar RR kinematic chains is presented. The methodology uses an analytic representation of the planar RR dyad's rigid body constraint equation in combination with an algebraic geometry formulation of the exact synthesis for three prescribed positions to yield designs that exactly reach the prescribed pick and place positions while approximating an arbitrary number of guiding positions. The result is a dimensional synthesis technique for mixed exact and approximate motion generation for planar RR dyads. A solution dyad may be directly implemented as a 2R open chain or two solution dyads may be combined to form a planar 4R closed chain, also known as a planar four-bar mechanism. The synthesis algorithm utilizes only algebraic geometry and does not require the use of a numerical optimization algorithm or a metric on elements of SE(2); the group of planar displacements. Two implementations of the synthesis algorithm are presented; computational and graphical construction. Moreover, the kinematic inversion of the algorithm is also included. Two examples that demonstrate the synthesis technique are included.

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References

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Larochelle, P., 2012, “Synthesis of Spatial CC Dyads and 4C Mechanisms for Pick & Place Tasks With Guiding Locations,” Latest Advances in Robot Kinematics, Springer, New York, pp. 437–444.
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Figures

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Fig. 1

Planar RR dyad geometry and nomenclature

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Fig. 4

Five prescribed positions

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Fig. 6

The solution mechanism

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Fig. 7

The mechanism shown in the pick position

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Fig. 8

The mechanism shown in the place position

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Fig. 9

Eleven prescribed positions

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Fig. 10

The solution mechanism

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Fig. 11

The mechanism shown in the pick position

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Fig. 12

The mechanism shown in the place position

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