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Research Papers

Controlling the Movement of a TRR Spatial Chain With Coupled Six-Bar Function Generators for Biomimetic Motion

[+] Author and Article Information
Mark M. Plecnik

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

J. Michael McCarthy

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

1Corresponding author.

Manuscript received August 14, 2015; final manuscript received October 31, 2015; published online May 4, 2016. Assoc. Editor: Hai-Jun Su.

J. Mechanisms Robotics 8(5), 051005 (May 04, 2016) (10 pages) Paper No: JMR-15-1224; doi: 10.1115/1.4032105 History: Received August 14, 2015; Revised October 31, 2015

This paper describes a synthesis technique that constrains a spatial serial chain into a single degree-of-freedom mechanism using planar six-bar function generators. The synthesis process begins by specifying the target motion of a serial chain that is parameterized by time. The goal is to create a mechanism with a constant velocity rotary input that will achieve that motion. To do this, we solve the inverse kinematics equations to find functions of each serial joint angle with respect to time. Since a constant velocity input is desired, time is proportional to the angle of the input link, and each serial joint angle can be expressed as functions of the input angle. This poses a separate function generator problem to control each joint of the serial chain. Function generators are linkages that coordinate their input and output angles. Each function is synthesized using a technique that finds 11 position Stephenson II linkages, which are then packaged onto the serial chain. Using pulleys and the scaling capabilities of function generating linkages, the final device can be packaged compactly. We describe this synthesis procedure through the design of a biomimetic device for reproducing a flapping wing motion.

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References

Figures

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Fig. 1

This figure illustrates the wing gait of an accelerating black-billed magpie. (Reprinted with permission from Tobalske and Dial [36]. Copyright 1996 by the Company of Biologists Ltd.)

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Fig. 2

The links of a TRR spatial chain correlate to the bones of a bird's wing. (Magpie image is reprinted with permission from Tobalske et al. [37]. Copyright 1997 by John Wiley and Sons.)

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Fig. 3

A smooth trajectory of the wrist point is produced by fitting Fourier series to the discrete joint angle functions for ψA, ψB, ψC

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Fig. 4

The joint angle functions for (a) ψA, (b) ψB, (c) ψC, and (d) ψD. The discrete data curves were fitted with Fourier series functions. Eleven task points were chosen from the Fourier functions to synthesize a mechanism.

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Fig. 5

The addition of sprung joints creates a compliant hand wing design. Hard stops prevent dorsal flexure of the hand wing. The new segment lengths are l4 = 0.375, l5 = 2.125, l6 = 2.5, and l7 = 2.6.

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Fig. 6

A Stephenson II function generator in (a) the initial configuration and (b) the jth configuration

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Fig. 7

The linkages selected to mechanize the joint angle trajectories of the magpie wing. The linkage that generates (a) ψA=fA(ϕ) passes through seven task positions, (b) ψB=fB(ϕ) passes through nine task positions, (c) ψC=fC(ϕ) passes through eight task positions, and (d) ψD=fD(ϕ) passes through nine task positions.

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Fig. 8

Diagram of power transmission from the motor, through the function generators, to the joints

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Fig. 9

A prototype design for the function generator controlled magpie wing

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Fig. 10

The wingtip path (black) of the mechanized wing alongside the desired path (gray) interpreted from the data recorded in Fig. 1

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