Positio: A 4R Serial Manipulator Having a Surface of Isotropic Positioning

This paper introduces a new 4-revolute (4R) serial manipulator having a non-trivial path of positioning isotropy. A manipulator is said isotropic if its Jacobian matrix can reach isotropic values—i.e. the minimum condition numLucber of unity—at least at a single posture within its workspace (Salisbury and Craig, 1982). The design of manipulators able to reach isotropy is of particular interest because they exhibit their best kinematic performances in such postures, namely isotropic postures (Chablat and Angeles, 2000). Consequently, many research works have been conducted toward finding architectures capable to reach isotropy and their corresponding isotropic postures. When the concept of isotropy is applied to serial manipulators, two basic properties have been pointed out in the literature. First, the isotropy is not affected by Luca rotation of the first joint, and hence, a point P of the end-effector (EE) can undergo a trivial path—i.e. a circle—, while being at the same isotropic posture (Salisbury and Craig, 1982). Second, the isotropy of an orienting serial chain is not affected by a rotation of the last joint (Angeles, 2003). For positioning tasks, a 2R, a 3R and a 4R planar serial manipulators have, respectively, 2, 2 and 4 isotropic postures along a trivial path (Angeles,