Mechanism Analysis and Design

Kinematic Geometry

• Screw Theory

What is ?

The algebra and calculus of pairs of vectors, such as forces and moments and angular and linear velocity, that arise in the kinematics and dynamics of rigid bodies.

A mathematical formulation for the geometry of lines which is central to rigid body dynamics, where lines form the screw axes of spatial movement and the lines of action of forces.

A tool in robot mechanics, mechanical design, computational geometry and multi-body dynamics.

Chasles’ Theorem

The most general rigid body displacement can be produced by a translation along a line followed (or preceded) by a rotation about that line

Screw Motion

• Lie Group and Lie Algebra

Lie group

The foundations of the theory of continuous transformation groups

Lie algebra

Algebraic structures which were introduced to study the concept of infinitesimal transformations

Vibration Analysis via Screw Theory

• Main Goals

To consider vibration of mechanisms and robots that consist of several rigid bodies as infinitesimal motion in 2-dim or 3-dim space.

To analyze vibration of mechanisms and robots via screw theory.

To investigate that vibration centers of mechanisms and robots are the same as the centers(axes) of screw motions.

• Examples

2R serial robot

System and modeling

4-bar linkage

System and modeling