Research Papers

Kinematic Acquisition of Geometric Constraints for Task-Oriented Design of Planar Mechanisms

[+] Author and Article Information
Q. J. Ge

e-mail: Qiaode.Ge@stonybrook.edu
Computational Design Kinematics Lab,
Department of Mechanical Engineering,
Stony Brook University,
Stony Brook, NY 11794-2300

Hai-Jun Su

Department of Mechanical
and Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210

Feng Gao

State Key Laboratory of Mechanical
System and Vibration, Shanghai Jiao Tong University,
Shanghai 200240, China

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received March 8, 2010; final manuscript received April 6, 2012; published online October 19, 2012. Assoc. Editor: Andrew P. Murray.

J. Mechanisms Robotics 5(1), 011003 (Oct 19, 2012) (7 pages) Paper No: JMR-10-1029; doi: 10.1115/1.4007409 History: Received March 08, 2010; Revised April 06, 2012

A motion task can be given in various ways. It may be defined parametrically or discretely in terms of an ordered sequence of displacements or in geometric means. This paper studies a new type of motion analysis problem in planar kinematics that seeks to acquire geometric constraints associated with a planar motion task which is given either parametrically or discretely. The resulting geometric constraints can be used directly for type as well as dimensional synthesis of a physical device such as mechanical linkage that generates the constrained motion task. Examples are provided toward the end of the paper to illustrate how geometric constraints acquired can be used for task-oriented mechanism design.

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Fig. 3

A discrete set of planar displacements

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Fig. 2

A planar displacement

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Fig. 8

An counterclockwise traced ellipse with semiminor axis of ρ

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Fig. 1

Mechanism-centric versus task-oriented design. Here, “feasible constraints” refer to those constraints that are approximately compatible with a given motion task.

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Fig. 4

The solid curve near the origin O is a standard geometric constraint g, the solid curve G is transformed from g, and the dash curve V is the trajectory of moving point v

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Fig. 5

The circular constraint traced in counterclockwise direction

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Fig. 6

The counterclockwise traced circular arc with center angle θ

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Fig. 7

A line segment is represented as a closed curve traced in counterclockwise direction

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Fig. 13

The trajectories of points A, B, C, D, E, and the corresponding geometric constraints obtained from kinematic acquisition process

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Fig. 9

Basic geometric constraints and their generating mechanisms

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Fig. 10

A given four-bar mechanism with A0B0=3.8,A0A1=2.4,A1B1=5, and B0B1=4.6. As crank A0A1 rotates for 360 deg, the coupler link A1B1 undergoes a periodic closed motion

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Fig. 12

A, B, C, D, and E are the five points whose trajectories are identified to match the geometric constraints

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Fig. 11

The rigid body in shaded area follows the motion of the coupler of a four-bar mechanism approximately. The trajectories (dash curves) of four points A, B, C, and D on this rigid body are identified to optimally match the geometric constraints circle, arc, ellipse and a four-bar coupler curve (solid curves), respectively.




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