| Abstract: | The authors propose a method for the determination of singularities in motion and displacement functions for a seven degree-of-freedom manipulator. The manipulator is considered, hereby, as a set of six degree-of-freedom manipulators. It is proven that two types of singularities in motion can occur at link positions that are independent and dependent with respect to the trajectory to be executed. The relations between the structure of singularity equations and displacement equations are discussed. The derivation of displacement equations for a manipulator with singularities of the second type is based on the idea of modeling of a manipulator by two open kinematic chains and invariants that may be found for these chains. The inverse kinematic equations and the equations of singularities in motion have been derived using a symbolic computer program which can handle manipulators of general structure (with five, six, and seven degrees-of-freedom). This program is written in the Symbolic Computation Language REDUCE. |
