Workspace Analysis of 4R Manipulators With Various Degrees of Dexterity

For 4R manipulators and their various possible configurations, workspaces with full, partial, and zero dexterity are defined, and a procedure to determine them is developed. As examples, two 4R manipulators are analyzed. Subspaces with 2, 4, 6, and 8 configurations and various degrees of dexterity are found. Several points on the effect of geometrical parameters on the shape and extent of the boundary surfaces, subspaces, and number of configurations are discussed. An index for the evaluation of the degree of accessibility of the workspace of a manipulator is also proposed.