Automated Symbolic-Numeric Methods for E cient Kinematics Computation of Loops in Mechanical Systems

This paper describes an object-oriented implementation and extension of the algorithm described in [6] for nding and generating closed-form solutions in single-loop mechanisms featuring such closed-form solutions. In contrast to the previously mentioned approach, the present method relies purely on the result of geometric projections, without performing symbolical simpli cations. This makes it possible to compute the closed-form solutions in a rather short time without the need of employing algebraic packages such as Mathematica or Maple. By this, the approach is suitable for integration in CAD systems, where a compromise between fast solution generation and fast solution computation is required. Moreover, the approach allows one to cycle through all solutions of a mechanism featuring explicitly solvable kinematics.