The present paper takes a general approach to the dimensional synthesis of
mechanisms via second-order optimization techniques. The error function is
the same for any type of kinematic synthesis and is independent of the kine
matic configuration of the mechanism. Mechanisms are modelled by means of r
od-type finite elements, while the solution of syntheses is based on the ju
dicious choice of constraints. The optimization parameters are the lengths
of the rods making up the model. Two procedures are developed for minimizin
g the error function, each of second-order. The first is based on using a p
recise estimate of the first and second derivatives of the error function,
while the second involves a rougher estimate based on the assumption that t
he rods are uncoupled. By combining the two procedures in the iterative pro
cess, and by adopting a variable convergence tolerance, one can synthesize
mechanisms even when the initial dimensions are very different from those o
f an acceptable solution.