Kinematic and Static Analysis of Open-Loop Manipulators Using Linear Algebra

In this paper the instantaneous kinematics and statics of open loop n-degree-of-freedom manipulators are studied using linear algebra. First we relate reciprocal screw system to linear algebra. Algorithms based on linear algebra are then developed to (i) determine if instantaneous motion is admissible, (ii) compute least-squares joint rates for underdetermined linear system, and (iii) determine which part of an external wrench needs to be balanced by the actuators (or which part of the input torques generates output wrench) and which part creates link interaction forces.