Parallel mechanisms with variable compliance

Compliant mechanisms can be considered as planar/spatial springs having multiple degrees of freedom rather than one freedom as line springs have. The compliance of the mechanism can be well described by the stiffness matrix of the mechanism which relates a small twist applied to the mechanism to the corresponding wrench exerted on the mechanism.;A derivative of the spring wrench connecting two moving rigid bodies is derived. By using the derivative of the spring wrench, the stiffness matrices of compliant mechanisms which consist of rigid bodies connected to each other by line springs are obtained. It is shown that the resultant compliance of two compliant parallel mechanisms that are serially arranged is not the summation of the compliances of the constituent mechanisms unless the external wrench applied to the mechanism is zero.;A derivative of the stiffness matrix of planar compliant mechanisms with respect to the twists of the constituent rigid bodies and the spring parameters such as the stiffness coefficient and free length is obtained. It is shown that the compliance and the resultant wrench of a compliant mechanism may be controlled at the same time by using adjustable line springs.