SERIAL CHAINS OF SPHERICAL FOUR-BAR MECHANISMS TO ACHIEVE DESIGN HELICES

This paper presents a method for designing serial chains of spherical four-bar mechanisms that can achieve up to five design helices. The chains are comprised of identical copies of the same four-bar mechanism by connecting the coupler of the prior spherical mechanism to the base link of the subsequent spherical mechanism. Although having a degree of freedom per mechanism, the design methodology is based upon identically actuating each mechanism. With these conditions, the kinematic synthesis task of matching periodically spaced points on up to five arbitrary helices may be achieved. Due to the constraints realized via the spherical equivalent of planar Burmester Theory, spherical mechanisms produce at most five prescribed orientations resulting in this maximum. The methodology introduces a companion helix to each design helix along which the intersection locations of each spherical mechanisms axes must lie. As the mechanisms are connected by rigid links, the distance between the intersection locations along the companion helices is a constant. An extension to the coupler matches the points along the design helices. An approach to mechanically reducing the chain of mechanisms to a single degree of freedom is also presented. Finally, an example shows the methodology applied to three design helices.