Dynamic problems of parallel mechanisms

Abstract

This chapter introduces our research on some dynamics problems of parallel mechanisms. The first problem is about the over-determinate inputs. This is quite an interesting issue. In practice, there are many machines and animals that work with over-determinate input, i.e., their input-number is much bigger than their mobility number. How to set the inputs to be accordance and optimum distribute and to obtain the expectant motion acceleration is a challenge. For the second part of this chapter, we focus on the dynamic analysis, i.e., the kinetostatic analysis of parallel mechanisms. For a link with two revolute pairs, based on its free-body diagram, its unknown value is 10 for the force analysis, and each link has only six equilibrium equations in the spatial mechanism. As it is, this is insolvable directly. Some time more unknown values may appear; and even up to 130 and it needs to set a 130-order matrix for the 5-5R parallel mechanism. This is extremely difficult. To resolve this issue, we propose a new method based on the screw theory. This method will only require the setting of a six-order matrix each time the dynamics problem can be readily solved. Moreover, in the following examples we can find the screws, their reciprocal screws, and their corresponding transformations each other, these are very interesting.