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Research Papers

# A Maneuver Based Design of a Passive-Assist Device for Augmenting Active Joints

[+] Author and Article Information
W. Robert Brown

e-mail: wrbrown@umich.edu

A. Galip Ulsoy

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received May 31, 2012; final manuscript received February 21, 2013; published online June 10, 2013. Assoc. Editor: Andrew P. Murray.

J. Mechanisms Robotics 5(3), 031003 (Jun 24, 2013) (11 pages) Paper No: JMR-12-1068; doi: 10.1115/1.4024237 History: Received May 31, 2012; Revised February 21, 2013

## Abstract

This paper describes a novel, general methodology for designing a parallel, passive-assist device to augment an active system using optimization based on a known maneuver of the active system. Implementation of the passive-assist device can result in an improvement in system performance with respect to efficiency, reliability, and/or utility. The methodology is demonstrated with a torsional spring designed to minimize energy consumption of a prototypical unmanned ground vehicle robot arm. Initial results indicate that this procedure can reduce maximum required torque by $~50%$ and energy consumed by as much as 25%. The proposed method is experimentally verified and compared to other state-of-the-art design approaches.

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## Figures

Fig. 1

Depicts an unsprung, actuated mass (a), the same system augmented with a parallel spring (b), and the same system as (a) augmented with a spring in a serial configuration (c)

Fig. 2

The prescribed (a) angular position, θg, (b) velocity, θ·g, and (c) acceleration, θ··g, of the robot arm over the course of the experimental maneuver

Fig. 3

Depicts how the arm progresses through the maneuver prescribed in Fig. 2. The arm starts unloaded, at rest, and in a vertical position (a), lowers (b), stops and remains at rest in a horizontal configuration (c), is loaded while still at rest (d), raises the load (e), and finishes the maneuver loaded, at rest, and back in a vertical configuration (f).

Fig. 4

Torque is supplied from the motor (not shown) to the input shaft, (a), which drives the worm, (b), via a gear head. For each revolution of the worm, the worm gear advances one tooth. The worm gear applies a moment to the output shaft parallel to a torsion spring, (c), to maneuver the arm, (d).

Fig. 5

Compares the experimental electrical power and motor torque profiles to the simulated profiles with and without a spring for the maneuver in Fig. 2. The simulated and experimental results are qualitatively similar and adding a well designed spring can significantly reduce the maximum required motor torque, peak electrical demand, and total energy consumed over the entire maneuver despite an increase in the power consumption at the beginning of the trajectory.

Fig. 6

The error in (a) position and (b) velocity, and (c) the command voltage of an experimental trial with no spring. The command voltage is comprised of feed-forward information on the prescribed maneuver as well as proportional-derivative (PD) control. Superior controller design could reduce fluctuations in the experimental results and decrease dynamic lag at the beginning of the ascent phase.

Fig. 7

overlays the experimental electrical power profile (solid) onto three simulated power profiles that show the effect of variation of kinetic friction within the worm gear transmission. The three simulated profiles depict the predicted power based on the mean value of friction (medium dash), the mean plus two standard deviations (long dash), and the mean minus two stand deviations (short dash).

Fig. 8

Depicts the energy consumed to execute the maneuver defined in Sec. 2.1 as a function of the gear ratio, n. Figure 8(a) corresponds to the UGV model simulated in Ref. [30], while Fig. 8(b) corresponds to the experimental model described in Sec. 2. The dashed line is the energy consumed by a no-spring design, while the solid line is the energy consumed with a spring design optimized for the specific gear ratio.

Fig. 9

The amount of energy saved (%) by the addition of a spring optimized for a specific maneuver varies as the maneuver being performed deviates from the maneuver used for design, +. The spring provides a varying degree of assistance so long as the lifted load does not drop too far below the load the spring was design for, at which point the spring decreases the systems performance.

Fig. 10

The angular position of a distribution of 10,000 trajectories. The contours correspond to deviation from the mean trajectory. The innermost contour contains the central 25% of trajectories, while the outermost contour contains 99% of all trajectories.

Fig. 11

Plots the experimentally found values of the coefficient of kinetic friction within the worm gear transmission. The data are organized by operating state. There is no statistical difference to the mean value of μ based on speed, direction of motion, or side of engagement.

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