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Research Papers

Optimal Transmission Ratio Selection for Electric Motor Driven Actuators With Known Output Torque and Motion Trajectories

[+] Author and Article Information
Harrison L. Bartlett

Mechanical Engineering,
Vanderbilt University,
Nashville, TN 37235
e-mail: harrison.l.bartlett@vanderbilt.edu

Brian E. Lawson

Mem. ASME
Mechanical Engineering,
Vanderbilt University,
Nashville, TN 37235
e-mail: brian.e.lawson@vanderbilt.edu

Michael Goldfarb

Professor
Fellow ASME
Mechanical Engineering,
Vanderbilt University,
Nashville, TN 37235
e-mail: michael.goldfarb@vanderbilt.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 12, 2016; final manuscript received March 9, 2017; published online June 28, 2017. Assoc. Editor: Ardalan Vahidi.

J. Dyn. Sys., Meas., Control 139(10), 101013 (Jun 28, 2017) (7 pages) Paper No: DS-16-1345; doi: 10.1115/1.4036538 History: Received July 12, 2016; Revised March 09, 2017

This paper presents a method for selecting the optimal transmission ratio for an electric motor for applications for which the desired torque and motion at the transmission output are known a priori. Representative applications for which the desired output torque and motion are periodic and known include robotic manipulation, robotic locomotion, powered prostheses, and exoskeletons. Optimal transmission ratios are presented in two senses: one that minimizes the root-mean-square (RMS) electrical current and one that minimizes the RMS electrical power. An example application is presented in order to demonstrate the method for optimal transmission ratio selection.

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Figures

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Fig. 1

The electromechanical actuator model treated here is split into three components: the motor, transmission, and load, each with associated constants and parameters

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Fig. 2

(a) The bond graph of a mechanical transmission with state-dependent impedances associated with its power source and known output efforts and flows and (b) the same system reflected into the output domain

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Fig. 3

The bond graph of a direct current motor and a mechanical transmission driving a load with desired kinematics and kinetics. The motor electrical inductance is assumed to be negligible.

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Fig. 4

Desired output dynamics of robotic ankle prosthesis actuator for dorsiflexion of the ankle during level ground walking: (a) ankle angle, (b) ankle angular velocity, (c) ankle angular acceleration, and (d) ankle torque

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Fig. 5

Actuator RMS current, peak current, and RMS power plotted against transmission ratio with feasible transmission bounds marked by vertical dashed lines. Dark-dashed lines indicate thermal bounds, gray vertical dashed lines indicate a torque or speed limitation, and the horizontal dashed lines are the motor's specified maximum continuous current. Current values are plotted against the left y-axis, while power values are plotted against the right y-axis. Two motors executing the same task are plotted in this figure: (a) EC 16 8 W (The upper thermal bound is off the right end of the plot) and (b) EC 45 12 W.

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