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پایان نامه دکترا
Dynamic balancing of linkages by algebraic methods
Brian Moore
Johannes-Kepler University Linz, Austria
Research Institute for Symbolic Computation
Abstract
A mechanism is statically balanced if, for any motion, it does not exert
forces on the base. Moreover, if it does not exert torques on the base, the
mechanism is said to be dynamically balanced. In 1969, Berkof and Lowen
showed that in some cases, it is possible to balance mechanisms without
adding additional components, simply by choosing the design parameters
(i.e. length, mass, centre of mass, inertia) in an appropriate way. For the
simplest linkages, some solutions were found but no complete characterization
was given.
The aim of the thesis is to present a new systematic approach to obtain
such complete classifications for 1 degree of freedom linkages. The method is
based on the use of complex variables to model the kinematics of the mechanism.
The static and dynamic balancing constraints are written as algebraic
equations over complex variables and joint angular velocities. After elimination
of the joint angular velocity variables, the problem is formulated as
a problem of factorisation of Laurent polynomials. Using computer algebra,
necessary and sufficient conditions can be derived.
Using this approach, a classification of all possible statically and dynamically
balanced planar four-bar mechanisms is given. Sufficient and necessary
conditions for static balancing of spherical linkages is also described and a
formal proof of the non-existence of dynamically balanced spherical linkage
is given. Finally, conditions for the static balancing of Bennett linkages are
described.
Dynamic balancing of linkages by algebraic methods
