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Research Papers

Design of Statically Balanced Spatial Mechanisms With Spring Suspensions

[+] Author and Article Information
Po-Yang Lin

 Department of Mechanical Engineering, National Taiwan University, Taipei 106, Taiwand96522034@ntu.edu.tw

1

Corresponding author.

J. Mechanisms Robotics 4(2), 021015 (Apr 25, 2012) (7 pages) doi:10.1115/1.4006522 History: Received April 15, 2011; Revised March 04, 2012; Published April 25, 2012; Online April 25, 2012

This paper proposes a general approach for designing spatial statically balanced mechanisms with articular joints utilizing ideal zero-free-length springs. The proposed statically balanced mechanism can counterbalance the gravitational forces and provides a perfect static equilibrium at any configuration. The method of the paper is based on the energy approach, and a generalized coordinate system is developed to define the configuration of a spatial mechanism and to be a vector basis for the derivation of potential energy. By incorporating the gravitational forces and the spring forces into the system, the stiffness matrix of a spring-loaded mechanism is proposed. The perfect static balance is observed when the stiffness matrix is a diagonal matrix, from which, the design equations can be readily obtained. The closed-form solution of spring design parameters of a statically balanced, spatial, three-articular arm is obtained as a design example. The simulations of the conceptual design are performed by commercial computer software, and the static equilibrium of a quasi-static continuous motion is verified.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

The position of a point Pi on body i with respect to a local frame and a global frame

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Figure 2

The position vector from point O1 to point Pi with the mechanism basis

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Figure 3

A segment of a kinematic chain with mass centers on lines passing through articular points

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Figure 4

Elastic element s connected to links i and j

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Figure 5

The spatial statically balanced SSS arm

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Figure 6

The time history plotting of the joint torques in the spatial statically balanced SSS arm (a) before and (b) after spring balancing

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Figure 7

The spatial statically balanced RSR arm with two spring suspensions

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