Research Papers

A Cyclic Robot for Lower Limb Exercise

[+] Author and Article Information
Brian P. DeJong1

 School of Engineering and Technology, Central Michigan University, Mount Pleasant, MI 48859b.dejong@cmich.edu

J. Edward Colgate

Department of Mechanical Engineering,  Northwestern University, Evanston, IL 60208colgate@northwestern.edu

Michael A. Peshkin

Department of Mechanical Engineering,  Northwestern University, Evanston, IL 60208peshkin@northwestern.edu

As defined by the corresponding authors.

This problems holds for any configuration where the two crank arms are on the same side of the horizontal axis.

The path has some vertical motion because the distal Crank Arm links are not the same length.

The flat top boundary of the set is the result of the maximum possible pedal height based on the Modified Pantograph dimensions.

In actuality, it will vary slightly because of the shuffling of energy to and from the links’ masses, and to and from the user.


Corresponding author.

J. Med. Devices 5(3), 031006 (Aug 15, 2011) (9 pages) doi:10.1115/1.4004648 History: Received July 19, 2010; Revised June 07, 2011; Published August 15, 2011; Online August 15, 2011

This paper presents the design and simulation of a cyclic robot for lower-limb exercise robots. The robot is designed specifically for cyclic motions and the high power nature of lower-limb interaction—as such, it breaks from traditional robotics wisdom by intentionally traveling through singularities and incorporating large inertia. Such attributes lead to explicit design considerations. Results from a simulation show that the specific design requires only a reasonably sized damper and motor.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Comparison between lower-limb exercise robots and other devices

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Figure 2

Sample foot paths for exercise (user is facing to the left). Running and walking paths were obtained by analyzing video available from Ref. [22] and by modifying a figure in Ref. [23]; other paths are as modeled.

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Figure 3

User forces measured on Life Fitness X5, for a 104 kg user, during normal operation, at approximately 60 rpm. User is facing to the left. (a) Forces versus time (b) Force direction within one cycle (path as modeled).

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Figure 4

Foot pedal on the sample path. The arrows show separation of path actuation (perpendicular) from inertial and damping forces (parallel).

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Figure 5

The specific design, colored for the three subsystems

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Figure 6

The sample pedal path in the four spaces

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Figure 7

Sample paths resulting from constant phases (i.e., the angles between the crank arms). (a) Phase = 0. (b) Phase = π. (c) Phase = π/6.

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Figure 8

Phases for paths. (a) Set of constant-phase paths. (b) One desired path, with resulting phase values.

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Figure 9

Path boundary due to singularity at (a) θ1  = π, (b) θ1  = 0

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Figure 10

Sample valid paths that touch all four boundaries

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Figure 11

Apparent inertia (as a ratio of flywheel inertia) along the path

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Figure 12

Torques on the device at the timestep when the user’s torque was maximum. Note that at this timestep, τuser is near perpendicular to the path.

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Figure 13

Power requirements of actuators at 1-2 or 3-4, for two cycles of the path

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Figure 14

Speed-torque curves for actuators on 1-2 versus 3-4




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