Symbolic Computation Techniques Research Articles

Use of symbolic computation in robotics education

An application of symbolic computation in robotics education is described. A software package is presented which combines generality, user interaction, and user-friendliness with the systematic usage of symbolic computation and artificial intelligence techniques. The software utilizes MACSYMA, a LISP-based symbolic algebra language, to automatically generate closed-form expressions representing forward and inverse kinematics solutions, the Jacobian transformation matrices, robot pose error-compensation models equations, and Lagrange dynamics formulation for N degree-of-freedom, open chain robotic manipulators. The goal of such a package is to aid faculty and students in the robotics course by removing burdensome tasks of mathematical manipulations. The software package has been successfully tested for its accuracy using commercially available robots.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Topological and kinematical study of tree structure robot manipulators: Symbolic computation technique

Tree structure robot manipulators have been seldomly studied because of the complexity of their topological structures compared to simplechain type. This paper presents the topological and kinematical analysis of such systems. The kinematic analysis is based on the idea of decomposing the whole model to a number of submodels, one for each arm of the tree. A complete symbolic kinematical analysis of a five-link structure with two end-effectors is presented. The necessary number of arithmetic operations for computing each model is also computed. This example shows the effectiveness of the approach used for kinematic analysis of this type of robot manipulators.

Application of symbolic computation to fracture mechanics design.

As fracture mechanics is evolving very rapidly, it is becoming more and more difficult for a designer to find an appropriate formula or solution for his problem among an overwhelming amount of fracture mechanics information. Although designs are carried out using only linearelastic fracture mechanics in most cases, it is still difficult because there are many complicated mathematical formula and because it is often the case that he has to combine several solutions in order to solve his problem. Therefore, if we could provide a system to where, when and how to use fracture mechanics in designs, it is expected that fracture mechanics will be used much more easily and therefore more extensively. This paper describes an attempt to develop such a system utilizing symbolic computation techniques.

Applications of symbol manipulation in theoretical physics

This paper surveys the applications of symbolic computation techniques to problems in theoretical physics. Particular emphasis is placed on applications in quantum electrodynamics where the most activity has occurred.