Analysis for a planar 3 degree-of-freedom parallel mechanism with actively adjustable stiffness characteristics

A planar three degree-of-freedom parallel manipulator has been extensively studied as the fundamental example of general parallel manipulators. It is proven from previous work (Kim, et. al., 1996) that when three identical joint compliances are attached to the three base joints of the mechanism in its symmetric configurations, this mechanism possesses a completely decoupled compliance characteristic at the object space, which is the important operational requirement for an RCC device. In this work, we are concerned with the adjustability of the output compliance matrix of this mechanism, by employing redundancy on either joint compliances or on actuators. Two approaches are suggested to achieve this purpose. In the first approach, the stiffness modulation is achieved through purely redundant passive springs or decoupled feedback stiffness gains. In the second approach, stiffness modulation is achieved through antagonistic actuation of the system actuators. General stiffness models are derived for both cases. Based on these stiffness models, stiffness modulation algorithms are formulated. The capability of actively adjustable stiffness will be very effective in several robotic applications.