Some explicit relations in kinematics of mechanisms. (English) Zbl 0987.70002

Lerbet, Jean

Mech. Res. Commun. 27, No. 6, 621-630 (2000).

Summary: Using Lie group theory, we derive some explicit relations in kinematics of mechanisms without introducing coordinates. After a presentation of the mathematical tools, the kinematics of closed mechanisms is studied using Lie group language. We give a family of relations between dependent and independent variables and their derivatives which may be useful for linearization or for numerical integration. Two examples illustrate these relations.

MSC:

70B15	Kinematics of mechanisms and robots
70G65	Symmetries, Lie group and Lie algebra methods for problems in mechanics

Keywords:

differential geometry; closure function; Taylor expansion; Lie group theory; explicit relations; kinematics of mechanisms; closed mechanisms