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Research Papers

# Effect of Torque-Velocity Relationship on Manipulability for Robot Manipulators

[+] Author and Article Information
Tetsuyou Watanabe

School of Mechanical Engineering, College of Science and Engineering,  Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan e-mail: te-watanabe@ieee.org

J. Mechanisms Robotics 3(4), 041007 (Sep 27, 2011) (9 pages) doi:10.1115/1.4004895 History: Received December 03, 2010; Revised March 26, 2011; Published September 27, 2011; Online September 27, 2011

## Abstract

This paper presents novel manipulability analysis for robotic manipulators, taking the effect of generating joint torques on generable joint velocities and vice versa into consideration. The conventional manipulability is analysis in velocity domain and cannot concern force effect such as gravity of payload and external forces exerted on the endeffector. Gravitational force has been regarded that it just changes the origin of the manipulability ellipsoid expressing the set of generable tip velocities, and its evaluation (its volume) does not change. However, if robot grasps a heavy object, the robot cannot move with the same speed as the case of grasping a light object, because the power of the robot is limited. It indicates that the robot performance evaluation by conventional manipulability has serious problem that the force effect cannot be included. The power of the robot is determined by the operation range of every actuator, which tells us the relationship between generating torque/velocity and addable velocity/torque. Then, this paper presents novel manipulability analysis which can take the force effect into consideration, based on the torque-velocity relationship. This analysis shows that manipulability is influenced by payload, gravitational force, and external forces.

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## Figures

Figure 1

Operation range of torque and velocity (maxon DC motor Amax16 (2 W) with gear (ratio: 371:1)); supposing to control with nominal voltage

Figure 2

Manipulability for two-link planar manipulator: (a) original manipulability ellipsoid and (b)–(f) new manipulability polyhedron (TVMP): (b) mp  = 0.0, (c) mp  = 0.1, (d) mp  = 0.2, (e) mp  = 0.3, and (f) mp  = 0.4

Figure 3

Manipulability measures for two-link planar manipulator

Figure 4

Target system in three-dimensional space

Figure 5

New manipulability polyhedra (TVMP) for the manipulator shown in Fig. 4: (a) q2  = 0, (b) q2  = −π/16, (c) q2  = −π/8, (d) q2  = −3π/16, and (e) q2  = −π/4

Figure 6

Manipulability measures for the manipulator shown in Fig. 4: (a) αν , (b) αmaxall, and (c) αmax

Figure 7

New force manipulability polyhedra for the manipulator shown in Fig.4: (a) q2  = 0, (b) q2  = −π/16, (c) q2  = −π/8, (d) q2  = −3π/16, and (e) q2  = −π/4

Figure 8

Force manipulability measures for the manipulator shown in Fig. 4: (a) βν , (b) βmaxall, and (c) βmax

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