An algebraic study of linkages with helical joints
This work solves a specific problem in kinematics for researchers in mechanical engineering and algebra, but it is incremental as it extends existing methods to a previously unaddressed case.
The paper tackled the problem of studying linkages with helical joints, which previous algebraic methods failed to address due to non-algebraic relations, and achieved a classification of mobile closed 5-linkages with revolute, prismatic, and helical joints.
Methods from algebra and algebraic geometry have been used in various ways to study linkages in kinematics. These methods have failed so far for the study of linkages with helical joints (joints with screw motion), because of the presence of some non-algebraic relations. In this article, we explore a delicate reduction of some analytic equations in kinematics to algebraic questions via a theorem of Ax. As an application, we give a classification of mobile closed 5-linkages with revolute, prismatic, and helical joints.