USING THE AUSDEHNUNGSLEHRE AND MATHEMATICA TO DETERMINE THE UNKNOWN PARAMETERS
OF GRASSMANN CHAIN MECHANISMS WITH TWO AND THREE INPUT SOURCES

Gloria Bitterfeld

Swinburne University of Technology, School of Mechanical and Manufacturing
Engineering, PO Box 218, Hawthorn, 3122, Victoria, Australia

ABSTRACT: The Grassmannian mathematical system, well known as the
Ausdehnungslehre together with the symbolic computational program Mathematica
is used to synthesise a class of planar mechanisms, named Grassmann Mechanisms.
The objective of investigating Grassmann Mechanisms is to be able to compute
easily the design parameters of the mechanism from their precision points.

Mechanisms in this class have only moving links rotating on pivots.  The paper
reports on a type of synthesis result of Grassmann Mechanism with two input
sources using four precision points.  Extending this type of Grassmann
Mechanism the paper implements a new type of mechanism named Grassmann Chain
Mechanism which has three input sources.  A synthesis result of this type of
mechanism is also presented using two precision points and two precision lines
for the last mechanism of the chain and four precision points for the join
mechanism.  Numerical examples are presented to justify the simplicity of the
Grassmannian method to mechanism design.