Analytical Dynamics of Open Kinematic Chains

Abstract

Consider a system of N particles: {S} = {P₁, P₂, ... P _i ... P _N }. The position vector of the ith particle in the Cartesian reference frame is r _i = r _i (x _i , y _i , z _i ) and can be expressed as

r _i = x _i ı+y _i j+z _i k, i = 1, 2, ..., N.

The system of N particles requires n = 3N physical coordinates to specify its position. To analyze the motion of the system in many cases, it is more convenient to use a set of variables different from the physical coordinates.