On the elliptic path of an endeffector for an anthropomorphic manipulator
Abstract
The application of an anthropomorphic manipulator with an endeffector traveling along a path whose projection on the rzplane of a cylindrical coordinate system as an ellipse is considered. It is shown that the coordinates along the path may be expressed in terms of (pi t + zeta), where zeta(t) is an unknown function of time to be determined for an optimal velocity distribution along the path by minimizing the total energy used by the manipulation system. As a computational technique, zeta is expressed as a finite series, satisfying the boundary conditions at two terminal points, with the optimal coefficients lambda sub n, f sub n, and k sub n to be evaluated. Two different values for numerical illustration are selected: the smallest value for the problem under investigation, and 0.995 (close to the largest value). It is found that the energy optimization is for the most part due to lambda sub 1 and f sub 1, and consequently a rapid convergence is ensured.
 Publication:

International Journal of Robotics Research
 Pub Date:
 1984
 Bibcode:
 1984IJRR....3...51S
 Keywords:

 Actuators;
 End Effectors;
 Manipulators;
 Numerical Control;
 Robotics;
 Three Dimensional Motion;
 Trajectory Control;
 Biodynamics;
 Computer Aided Manufacturing;
 Degrees Of Freedom;
 Dynamic Models;
 Elliptic Functions;
 Guidance (Motion);
 Kinematic Equations;
 Optimization;
 Positioning;
 Engineering (General)