Innovative equation management techniques for implementation in kinematics and dynamics courses

The scope of this paper is the description of techniques and algorithms which engineers use in mathematically modeling physical systems. This work builds on recently developed algorithms that can be used to guide students in solving and understanding the mathematical modeling of physical systems. The techniques have been developed for general use in a number of applications, especially in a kinematics and dynamics course. The techniques allow easy manipulation of equations and systems of governing equations in complex situations. The algorithms and techniques generally guarantee, and actually restrict, the student to specify a design variables set in a manner that solutions are possible. This paper documents that the selection of design variables is difficult anti-intuitive and, in some cases, it is humanly impossible to generate all of the possible combinations of constraints. While currently the algorithms are implemented in a computer program, the techniques can also be applied to hand calculations. By way of demonstration, a kinematics and dynamics design software program was developed which exemplifies the usefulness and, more importantly, the key benefits of the developed algorithms. The intention is to show that the algorithms are applicable to any set of equations and can be used to enhance students problem solving abilities.