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RESEARCH PAPERS

# Velocity Effects on Robotic Manipulator Dynamic Performance

[+] Author and Article Information
Alan P. Bowling

Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556abowling@nd.edu

ChangHwan Kim

Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556ckim@nd.edu

J. Mech. Des 128(6), 1236-1245 (Jan 09, 2006) (10 pages) doi:10.1115/1.2336255 History: Received February 11, 2005; Revised January 09, 2006

## Abstract

This article explores the effect that velocities have on a nonredundant robotic manipulator’s ability to accelerate its end-effector, as well as to apply forces/moments to the environment at the end-effector. This work considers velocity forces, including Coriolis forces, and the reduction of actuator torque with rotor velocity described by the speed-torque curve, at a particular configuration of a manipulator. The focus here is on nonredundant manipulators with as many actuators as degrees-of-freedom. Analysis of the velocity forces is accomplished using optimization techniques, where the optimization problem consists of an objective function and constraints which are all purely quadratic forms, yielding a nonconvex problem. Dialytic elimination is used to find the globally optimal solution to this problem. The proposed method does not use iterative numerical optimization methods. The PUMA 560 manipulator is used as an example to illustrate this methodology. The methodology provides an analytical analysis of the velocity forces which insures that the globally optimal solution to the associated optimization problem is found.

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## Figures

Figure 2

PUMA 560 DCS for ∣ω∣=∣f∣=∣m∣=0. The intercepts for this surface are {8.5m∕s2,76.5rad∕s2,0.375m∕s}.

Figure 8

PUMA 560 DCS for ∣f∣=∣m∣=0 and ∣ω∣=η∣v∣ where η∊{1,4,8,15,∞}

Figure 1

Purely quadratic approximations to a linear speed-torque curve

Figure 3

PUMA 560 configuration and worst-case directions

Figure 4

A spherical coordinate for translational(angular) velocity space

Figure 5

PUMA 560 DCC. The option 1, 2, 3a, and 3b curves were obtained by evaluating the DCE at η∊{0,0.5,1,2,3,4,6,8,10,12.5,15,30,50.6,100,1000,∞}.

Figure 6

PUMA 560 DCC from C(ϑ). The option 1–3b and case 4 curves were obtained by evaluating the DCE at η∊{0,0.5,1,2,3,4,6,8,10,12.5,15,30,50.6,100,1000,∞}.

Figure 7

PUMA 560 DCS for ∣f∣=∣m∣=0 and ∣ω∣=η∣v∣ where η∊{0,1,4,8,15}

## Errata

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