The objective of this research work is the study and development of techniques
for the design and synthesis of planar-linkage mechanisms. The synthesis of mechanisms
consists in finding the suitable mechanism for a given movement. Particularly,
this thesis deals with the problem of synthesis of mechanisms starting from the initial
specifications or requirements of design, that is to say, starting from zero. Consequently,
it is necessary to determine the number and type of components, and the
connectivity between them (type synthesis); and then to calculate the dimensions of
the components, pivots positions, and the control parameters of the kinematic pairs
of the input movement (dimensional synthesis).
This thesis deals with the kinematic synthesis of position, whose problem consists
in determining the dimensions of a mechanism that satisfies a desired set of
displacements and rotations in certain points of a mechanism and for certain instants
of simultaneity. This specification is called kinematic task. The allowed space –for
the solution mechanism and the development of the task– is a very common requirement
that restricts the solutions to obtain. The problem is highly non-linear.
Besides, since it includes the selection of the topology to dimension, it constitutes a
discrete problem of combinatorial complexity.
In order to solve this difficult problem, it is proposed to use a representation of
the mechanism based on the Finite Elements Method and Graph Theory, managing
to preserve and unify both representations to integrate the synthesis into its subsequent
stages of detailed analysis and optimization of the mechanism. The original
theoretical aspects presented in this thesis are:
The development of a new identifier of isomorphism of mechanisms and its use
in the enumeration of kinematic chains and different atlases of mechanisms.
The exhaustive enumeration of topologies using sub-graphs search to satisfy
structural requirements from the beginning of the design process.
The automatic decomposition of the closed-loop topologies into single open
chains to solve their dimensional synthesis using analytical equations expressed
by complex-numbers.
For the dimensional synthesis, all combinations of single open chains (some of
them with multiple solutions) are automatically computed. Among them, that
solution which minimizes the summation of link sizes subjected to some design
restrictions is retained. In the cases in which there are free parameters, a zeroorder
optimization technique based on Genetic Algorithms with penalization
of restrictions is applied to sweep the design space.
The modifications for extending the methodology to the design of flexible
mechanisms using Rigid-Body Replacement methods are developed and analyzed.
As the final result of the application of this technique, it is obtained a list of
alternatives that constitute good initial conditions for subsequent gradient-based
optimization already available in commercial software. Throughout the thesis, various
test and validation examples are provided, showing the capacity of the inventive
tool developed.