Comparison of methods for developing the dynamics of rigid-body systems

Several approaches for developing the equations of motion for a three-degree-of-freedom PUMA robot were compared on the basis of computational efficiency (i.e., the number of additions, subtractions, multiplications, and divisions). Of particular interest was the investigation of the use of computer algebra as a tool for developing the equations of motion. Three approaches were implemented algebraically: Lagrange's method, Kane's method, and Wittenburg's method. Each formulation was developed in absolute and relative coordinates. These six cases were compared to each other and to a recursive numerical formulation. The results showed that all of the formulations implemented algebraically required fewer calculations than the recursive numerical algorithm. The algebraic formulations required fewer calculations in absolute coordinates than in relative coordinates. Each of the algebraic formulations could be simplified, using patterns from Kane's method, to yield the same number of calculations in a given coordinate system.