Technical Briefs

Mechanical Issues Inherent in Antagonistically Actuated Systems

[+] Author and Article Information
Donald L. Russell1

Department of Mechanical and Aerospace Engineering, Carleton University, 1125 Colonel By Drive, Ottawa, ON, K1V 0W6, Canadadrussell@mae.carleton.ca

Megan McTavish

Canadian Intellectual Property Office, Industry Canada, Place du Portage I, 50 Victoria St., Room C-114, Gatineau, Quebec, Canada K1A 0C9

Chad E. English

 Neptec Design Group Ltd., 302 Legget Drive, Ottawa, Ontario, Canada K2K 1Y5

Note that the term stability is also occasionally used in discussing the tendency of a helical compression spring to buckle under a load (for example, see Sec. 36 in Ref. 31).


Corresponding author.

J. Mechanisms Robotics 1(4), 044501 (Sep 18, 2009) (8 pages) doi:10.1115/1.3212088 History: Received December 21, 2007; Revised April 09, 2009; Published September 18, 2009

The relationship between the stiffness properties of actuators configured in an agonist-antagonist configuration and the stiffness of the joint is simple but not intuitively obvious. In this paper, this relationship is investigated and it is shown that the stiffness properties (hardening or softening) of the joint depend on the second derivative of the individual actuator stiffness with respect to actuator displacement. Numerical examples are given to illustrate the relationship and two practical examples, in which the actuators stiffness arises from Belleville washers or from an air piston, are analyzed.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

An ideal mass-spring system used to clarify the impact of the stiffness properties inherent in the spring on the stability of the system

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Figure 2

An antagonistically actuated joint: (a) unloaded, (b) symmetric loading resulting in a possible stiffness change but no motion (assuming identical springs), and (c) an external load is applied. Note that, for clarity, the figures are aligned with the left hand end of the springs.

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Figure 3

A detailed illustration of the physical relationships

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Figure 4

Force and stiffness curves for various hardening springs: case A: linear stiffness curve, case B: stiffness curve concave up, case C: stiffness curve concave down; and for various softening springs: case D: linear stiffness curve, case E: stiffness curve concave up, and case F: stiffness curve concave down

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Figure 5

Belleville washer (34)

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Figure 6

Belleville washer force and stiffness relationships and the net overall joint stiffness. These results are for a AM204010 Belleville washer manufactured by Rolex (38) with D=1.57″, d=0.803″, t=0.0394″, and h=0.056″. The material is steel with E=200,000 MPa and μp=0.3.

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Figure 7

Air piston geometry

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Figure 8

Air piston force and stiffness curves. The plots are for an Airpot® model 2K160 (bore=0.627 in. or 1.59 cm, stroke=1.5 in. or 3.81 cm). The force model results agree with data from the airpot website (39).




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