An algebraic approach for system with multiple relative motions

作者：Abdel Baky Rashad A^*; Shafee Basma H

来源：Journal of Mechanical Science and Technology, 2013, 27(3): 621-628.

DOI：10.1007/s12206-013-0113-z

• Study's dual-line coordinates
• Lie algebra
• Line complex
• Screw motions

We present geometry and kinematic expressions for a kinematical system of multiple relative motions and containing a differentiable line-system using dual vector-matrix methods. This procedure enables us to obtain a generalization of the well-known three-pole theorem. In particular, for one-parameter spatial motions, the pitch of the helical motion is the translation multiplied by the tangent of the screw motion rotation. As a result, theoretical expressions for the direction of a line complex were revealed and used to examine a ruled surface traced out by a fixed line in a rigid body undergoing a screw motion of constant pitch.

• 出版日期2013-3