Analysis of spatial compliance behavior of coiled springs via screw theory

A new method is presented to describe and analyze the spatial compliance of coiled springs using screw theory. After an abbreviated description for the deformation of a beam element using screw theory, the spatial compliance density for a beam element is derived based on the fundamental material theory and reasonable assumptions, and the spatial compliance of the beam with finite length is obtained by integral. The spatial compliance of coiled springs is further analyzed using the spatial compliance density of the beam element. By calculating the eigencompliance and Bait's principle screws for the whole compliance of system, the compliance properties varying with the basic physical parameters of the system are illustrated in detail. The basic ideas can be used for the design and application of the coiled springs and the other compliant mechanisms with spatial compliant beam element.