COMPLETE FORWARD DISPLACEMENT SOLUTIONS FOR A CLASS OF 3-BRANCH PARALLEL MANIPULATORS

Forward displacement solutions are presented for a class of spatial parallel manipulators. In particular, considered are manipulators consisting of a platform supported through passive spherical joints by three branches, each branch having three-revolute joints forming its main arm. Solutions are described for arbitrary main-arm layouts and for all possible cases of redundant (nine, eight, and seven sensors) and non-redundant (six sensors) sensing of branch main-arm joint displacements. It is demonstrated that closed-form forward displacement solutions can be found for all cases of redundant sensing. Furthermore, it is shown that a closed-form solution can be obtained for one of the two possible cases of non-redundant sensing of the main-arm joint displacements. The only case of joint displacement sensing not allowing a closed-form forward displacement solution is two joints sensed per branch, a case that can be expressed as a 16th-order polynomial of a single variable. Due to the importance of having efficient and failure-safe solutions for the forward displacement problem, it is suggested that appropriate redundancy in displacement sensing should be an important consideration in the design of parallel manipulation devices. (c) 1994 John Wiley & Sons, Inc.