Coordinate Free Criteria for Testing the Linear Dependence of the Sets of Screws

Abstract

The verification of the linear dependence and the calculation of the rank of a set of screws are very important tasks in kinematics in the search for singular positions of open chains as as well as in the search for movability conditions of closed loop chains. This mathematical problem is generally solved by standard techniques of linear algebra using determinants of coordinates of the screws relative to more or less arbitrary bases (see for example Hunt [5], Sugimoto and Duffy [10] or Sugimoto [11], Wholhart [12]). However, such methods make no use at all of the specific algebraic structure which can be defined on the set of screws and, as for any coordinate method, the geometrical meaning of the result may be unclear.