| Abstract: | 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. © 1994 John Wiley & Sons, Inc. |
