Technical Briefs

A Closed-Form Solution for Minimizing the Cycle Time in Motion Programs With Constant Velocity Segments

[+] Author and Article Information
Forrest W. Flocker

e-mail: flocker_f@utpb.edu

Ramiro H. Bravo

e-mail: bravo_r@utpb.edu
Department of Engineering and Technology,
University of Texas of the Permian Basin,
4901 E. University, Odessa, TX 79762

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received March 22, 2012; final manuscript received June 5, 2012; published online November 19, 2012. Assoc. Editor: Ashitava Ghosal.

J. Mech. Des 135(1), 014502 (Nov 19, 2012) (7 pages) Paper No: MD-12-1170; doi: 10.1115/1.4007930 History: Received March 22, 2012; Revised June 05, 2012

An important need for some dynamic systems is to design a periodic motion program that has a constant velocity segment for a specified time. A few examples of such systems are cam-follower systems used in continuous motion manufacturing, linear actuators, space-based scanners, and industrial robots. In this paper, the closed-form solution is given for a motion program that minimizes the cycle time subject to user-specified limits on positive and negative acceleration and jerk. The main benefit of minimizing cycle time is to maximize the throughput. Two motion programs that address the problem are presented and critically examined. For general applicability, the solution is presented in dimensionless form and an example is given to show its implementation to a typical problem. Conclusions regarding the profiles are drawn and given.

Copyright © 2013 by ASME
Topics: Cycles , Acceleration
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Fig. 1

A typical machine with periodic output motion

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Fig. 2

Illustration of the problem to be solved

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Fig. 3

Dimensionless form of the problem

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Fig. 4

General form of the optimal acceleration

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Fig. 5

Follower kinematics for illustrative problem with trapezoidal acceleration: (a) follower position, (b) follower velocity, (c) follower acceleration, and (d) follower jerk

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Fig. 6

Cycle time as a function of jerk

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Fig. 7

Effect of jerk on kinematics: (a) follower position, (b) follower velocity, and (c) follower acceleration

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Fig. 8

Splined trapezoidal acceleration

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Fig. 9

Follower kinematics for illustrative problem with splined trapezoidal acceleration: (a) follower acceleration and (b) follower jerk

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Fig. 10

Spectral energy for the two acceleration functions used in the illustrative problem

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Fig. 11

Strength ratio of harmonic components—optimal to smoothed profiles

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Fig. 12

Spectral energy for trapezoidal acceleration at three jerk levels

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Fig. 13

Strength ratio of harmonic components—large to minimum jerk profiles



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