Generating the Isocurve Representation for Configuration Space of Mechanisms

This paper proposes an approach for generating a set of isocurves as a representation for configuration space (CS) of a mechanism. An isocurve here is a curve in CS with some parameters fixed. Compared with conventional methods like box approximations, sampling points, and boundary tessellations, the isocurve-based representation has some advantages in space parameterization and data management. This approach directly formulates the joint loop equations in the form of kinematic matrices, which does not need any extra conversions and solves the equations with an isocurve-tracing method applying ODE solvers. Since the isocurves are connected in certain orders with the guide isocurves in a lower-dimensional space, tracing all the isocurves only needs one initial solution point for an isolated solution component. In addition, the proposed approach includes an interference-handling step, which trims off the collision portions of the isocurves by checking their feasibility according to the previously defined half-space constraints, and a measure for identifying the forward direction at singular points where the first-order derivatives vanish. The approach is implemented through programming and the results for a few examples show its effectiveness.