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Design Innovation Paper

Planar Linkage Synthesis for Mixed Motion, Path, and Function Generation Using Poles and Rotation Angles1

[+] Author and Article Information
Ronald A. Zimmerman, II

Mem. ASME
Product Engineering Specialist
Research and Development,
Magna Seating,
Troy, MI 48098
e-mail: ron.zimmerman@magna.com

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received September 13, 2017; final manuscript received January 2, 2018; published online February 5, 2018. Assoc. Editor: Andrew P. Murray.

J. Mechanisms Robotics 10(2), 025004 (Feb 05, 2018) (8 pages) Paper No: JMR-17-1294; doi: 10.1115/1.4039064 History: Received September 13, 2017; Revised January 02, 2018

The kinematic synthesis of planar linkage mechanisms has traditionally been broken into the categories of motion, path, and function generation. Each of these categories of problems has been solved separately. Many problems in engineering practice require some combination of these problem types. For example, a problem requiring coupler points and/or poses in addition to specific input and/or output link angles that correspond to those positions. A limited amount of published work has addressed some specific underconstrained combinations of these problems. This paper presents a general graphical method for the synthesis of a four bar linkage to satisfy any combination of these exact synthesis problems that is not overconstrained. The approach is to consider the constraints imposed by the target positions on the linkage through the poles and rotation angles. These pole and rotation angle constraints (PRCs) are necessary and sufficient conditions to meet the target positions. After the constraints are made, free choices which may remain can be explored by simply dragging a fixed pivot, a moving pivot, or a pole in the plane. The designer can thus investigate the family of available solutions before making the selection of free choices to satisfy other criteria. The fully constrained combinations for a four bar linkage are given and sample problems are solved for several of them.

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References

Hall, A. S., Jr ., 1986, Kinematics and Linkage Design, Waveland Press, Prospect Heights, IL, p. 8.
Erdman, A. , and Sandor, G. , 1991, Mechanism Design Analysis and Synthesis Volume 1, Prentice Hall, Englewood Cliffs, NJ, pp. 7 and 37.
Erdman, A. , and Sandor, G. , 1991, Mechanism Design Analysis and Synthesis Volume 1, Prentice Hall, Englewood Cliffs, NJ, pp. 535–551.
Beyer, R. , 1963, The Kinematic Synthesis of Mechanisms, McGraw-Hill, New York, pp. 178–182.
Brake, D. , Hauenstein, J. , Murray, A. , Myska, D. , and Wampler, C. , 2016, “ The Complete Solution of Alt-Burmester Synthesis Problems for Four-Bar Linkages,” ASME J. Mech. Rob., 8(4), p. 041018. [CrossRef]
Tong, Y. , Myska, D. , and Murray, A. , 2013, “ Four-Bar Linkage Synthesis for a Combination of Motion and Path-Point Generation,” ASME Paper No. DETC2013-12969.
Kinzel, E. C. , Schmiedeler, J. P. , and Pennock, G. R. , 2006, “ Kinematic Synthesis for Finitely Separated Positions Using Geometric Constraint Programming,” ASME J. Mech. Des., 128(5), pp. 1070–1079. [CrossRef]
Mirth, J. , 2012, “ Parametric Modeling—A New Paradigm for Mechanisms Education?,” ASME Paper No. DETC2012-70175.
Zimmerman, R. , 2013, “ Planar Linkage Synthesis for Rigid Body Guidance Using Poles and Rotation Angles,” ASME Paper No. DETC2013-12036.
Zimmerman, R. , 2014, “ Planar Linkage Synthesis for Coupler Point Path Guidance Using Poles and Rotation Angles,” ASME Paper No. DETC2014-34058.
Zimmerman, R. , 2015, “ Planar Linkage Synthesis for Function Generation Using Poles and Rotation Angles,” ASME Paper No. DETC2015-46240.
Uicker, J. , Pennock, G. , and Shigley, J. , 2011, Theory of Machines and Mechanisms, Oxford University Press, New York, pp. 441–445.
McCarthy, J. M. , and Soh, G. S. , 2010, Geometric Design of Linkages, 2nd ed., Springer, New York, pp. 119–120.

Figures

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Fig. 1

Mixed synthesis case 2-1-1

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Fig. 2

Case 3-2-2 targets and solution

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Fig. 3

Function generation constraint

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Fig. 4

Motion generation constraint

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Fig. 5

Path generation constraint

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Fig. 6

Mixed synthesis sample constraints

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Fig. 7

Solution with prismatic joint

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Fig. 12

Case 2-4-2 pole and rotation angle constraints

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Fig. 13

Case 2-4-2 fixed and moving pivot lines intersections

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Fig. 11

Case 4-1-1 targets and solution

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Fig. 10

Case 2-4-2 targets and solution

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Fig. 9

Case 1-4-4 targets and solution

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Fig. 8

Two 3-2-2 configurations

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