Two 7-R manipulators which provide controllably dexterous workspace

The controllably dexterous workspace of a tool-point is defined. A type-synthesis process, based on screw theory and geometry, is extended to identify two 7-R robots, each of which can provide the controllably dexterous workspace. The identification process is confined to those robots that control the motion of the end-effector with seven series-connected joints, the axes for the outermost three of which are concurrent. The result for each is a suitable set of angle dimensions for the links of the arm, where the angle choices are limited to the values 0, ±π/2, and π. A geometric description of the kinematics for the dominant control function is included insofar as it is required to effect the identification. Also included are comments about motion planning in a controllably dexterous workspace