Structure and Property of the Singularity Loci of Gough-Stewart Manipulator

During the past two decades, parallel manipulator system has become one of the research attentions in robotics. This popularity has been motivated by the fact that parallel manipulators possess some specific advantages over serial manipulators, i.e., higher rigidity and load-carrying capacity, better dynamic performance and a simpler inverse position kinematics, etc. Among various manipulators, the best-known is the Gough-Stewart Platform (GSP) that was introduced as a tire performance (Gough 1956-57) and an aircraft simulator (Stewart 1965). One of the important problems in robot kinematics is special configuration or singularity. As to parallel manipulators, in such configurations, the end-effector keeps at least one remnant freedom while all the actuators are locked. This transitorily puts the end-effector out of control. Meanwhile, the articular forces may go to infinity and cause mechanical damages. Determination of the special configurations of the six-DOF Gough-Stewart parallel manipulators is a very important problem. It is one of the main concerns in the analysis and design of manipulators. The singularity analysis of parallel manipulators has attracted a great deal of attention in the past two decades. Hunt (1983) first discovered a special configuration for this manipulator that occurs when the moving triangle-platform is coplanar with two legs meeting at a vertex of the triangle, and all the six segments associated with six prismatic actuators intersect a common line. Fichter (1986) discovered a singularity of the parallel manipulator. That occurs when the moving platform rotates ψ =±π/2 around Z-axis, whatever the position of the moving platform is. That mechanism has a triangular mobile platform and a hexagonal base platform. It may be named a 3/6-GSP. Huang and Qu (1987) and Huang, Kong and Fang (1997) also studied the singularity of the parallel manipulator, whose moving and basic platforms are both semi-regular hexagons (6/6-GSP). It also occurs whenψ= ±π/2. Merlet (1988, 1989) studied the singularity of the six-DOF 3/6-GSP more systematically based on Grassman line geometry. He discovered many new singularities including 3c, 4b, 4d, 5a and 5b. 3c occurs when four lines of the six legs intersect at a common point; 4b occurs when five lines are concurrent with two skew lines; 4d occurs when all the five lines are in one plane or pass through one common point