Static balancing of spatial four-degree-of-freedom parallel mechanisms

The static balancing of four types of spatial four-degree-of-freedom parall el mechanisms or manipulators is discussed in this paper. Two static balanc ing methods, namely, using counterweights and using springs, are used. The first method leads to a mechanism with a stationary global center of mass a nd the second one leads to a mechanism with constant total potential energy (including the elastic potential energy stored in the springs). In both ca ses, the resulting mechanisms can be brought to static equilibrium in any c onfiguration of their workspace with zero actuator forces or torques. In or der to obtain the balancing conditions, the position vector of the global c enter of mass and the total potential energy of the mechanisms are first ex pressed as functions of the position and orientation of the platform and of the special fifth leg. Then, the conditions for static balancing are deriv ed from the expressions obtained. Examples are given to illustrate the appl ication of the results to the design of statically balanced spatial four-do f mechanisms or manipulators. (C) 1999 Elsevier Science Ltd. All rights res erved.