ON THE 3RD-ORDER FINITE SCREW SYSTEM - GENERAL DISPLACEMENT OF A LINE

The problem of displacing a line, being a part of a rigid body, from o ne spatial position to another is studied by using the concept of scre w matrix. It is known that there are infinity(2) possible screws to re alize such displacement; based on the definition of pitch given by Par kin, any one of the infinity(2) screws cannot be expressed as the line ar combination of three basis screws. In this paper an attempt is made towards a search of a new definition (expression) for pitch under whi ch the set of infinity(2) screws form a 3-system. It is shown that suc h expression for pitch exists and contains six arbitrary constants. By assigning some values to these constants two different but meaningful and valid expressions of pitch are obtained. These expressions are mo dified to include terms corresponding to Parkin's definition of pitche s. Explicit analytical expression of the 3-system is also discussed. ( C) 1998 Elsevier Science Ltd. All rights reserved.