Mathematical Concepts in Kinematics
This chapter explains characteristics of vectors, complex vectors, and complex vector forms. It discusses the formulation of vector-loop displacement, velocity, and acceleration equations using complex vectors. The chapter describes characteristics of point-based vectors and their application in mechanism motion equations. It reviews characteristics of linear simultaneous equations and their representation in matrix form. The chapter explores fundamental matrix operations and the identity matrix. It identifies matrix inversion and its application in solving linear simultaneous equations. The chapter also discusses intermediate and total spatial motion and their application in mechanism kinematics. It investigates the general transformation matrix and its application in the kinematic analysis of robotic manipulators. Vectors are commonly used in the formulation of mechanism equation systems because, being quantities that have both magnitude and direction, they can appropriately define mechanism motion. A linear equation is an equation that includes linear or first-order variables. A system of linear equations is collection of linear equations including the same variables.