Chapter 18 - Fundamentals of screw theory

Abstract

Screw theory is a mathematical tool developed by Robert Stawell Ball in the early 20th century for the purpose of studying rigid body statics and dynamics under the philosophy that entities such as forces, or velocities could be grouped into pairs of concatenated vectors capable of forming vectors of up to six dimensions. These vectors are governed by the rules of helicoidal vector fields and thus it is possible to determine the intensity of the vectors involved in the analysis. At the end of the 20th century, screw theory was revitalized and successfully applied in the analysis and synthesis of robotic manipulators including higher order kinematics analyses such as the jerk and jounce analyses. This chapter gives a brief review of basic concepts of screw theory that allow modeling the kinematic analysis of both serial and parallel manipulators. In that regard, reciprocal screw theory elegantly allows the determination of the input-output equations for velocity and acceleration in parallel manipulators.