Developable mechanisms on right conical surfaces. (July 2020) - Hyatt, Lance P.; Magleby, Spencer P.; Howell, Larry L.
Highlights: Spherical mechanisms can be mapped to conical surfaces. The Loop Sum Method finds the cone angle for spherical mechanisms. The position analysis of conical developable mechanisms uses axis-angle rotations. Projected angles connect conical and cylindrical developable mechanisms. Examples of four-bar and multiloop spherical mechanisms are presented. Abstract: An approach for designing developable mechanisms on a conical surface is presented. By aligning the joint axes of spherical mechanisms to the ruling lines, the links can be created in a way that the mechanism conforms to a conical surface. Terminology is defined for mechanisms mapped onto a right cone. Models are developed to describe the motion of the mechanism with respect to the apex of the cone, and connections are made to cylindrical developable mechanisms using projected angles. The Loop Sum Method is presented as an approach to determine the geometry of the cone to which a given spherical mechanism can be mapped. A method for position analysis is presented to determine the location of any point along the link of a mechanism with respect to the conical geometry. These methods are also applied to multiloop spherical mechanisms.