The Analytical Terminal Constraints Theory And Mathematics Method For The Degrees Of Freedom Of Spatial Parallel Mechanisms

The degree of freedom (DoF) is one of the most important concepts of mechanism and the key problem to be solved before a mechanism is designed. The universally accepted formula of DoF is that of Kutzbach Grübler's. Although the formula has been amended for times during the past century, many scholars often find it inconsistent with the reality when solving the DoF of certain mechanisms with the advent of complex spatial parallel mechanisms. Moreover, the DoFs of a system and its member are not differentiated in traditional formulas. As a result, they are easily confused in concept and not suited to the fast development of modern complex spatial parallel mechanisms. Therefore, it is urgent to establish a new theory of DoF for mechanisms to crack these problems.This dissertation puts forward the analytical terminal constraints theory and mathematical method for the DoF of spatial parallel mechanisms based on the uniform description of the kinematic and geometric constraints. Firstly, it points out that the concepts of the system's DoF and the end executor's DoF should be different. Secondly, it addresses that the concept of the end executor's DoF should covers the attributes of number, type and direction, which overcomes the difficulties when analyzing and designing the mechanisms. Similarly, it also reveals that the system's DoF should be the DoF of the mechanism with an end effector.In theory, to begin with investigating the terminal constraints of the kinematic chain, this dissertation establishes an analytical theory of constraints spaces for the DoF of the end effectors, puts forward the analytical method and formula for the mechanisms with end effectors. This theory can efficiently solve the DoF problems of the complex spatial parallel mechanisms that could not be correctly solved by the traditional ones. Within the theory, according to the invariable principle of terminal constraints, this dissertation presents equivalent theories of kinematic chains and the simple method to study the singularities of the parallel and hybrid mechanisms, based on which the conception of configuration degree of freedom (CDOF) is introduced and the singularity problems of the spatial parallel mechanisms are naturally transformed to be the analysis of the CDOF.In the application aspect of the theory, this dissertation discusses the workspace, the kinematics and dynamics of spatial parallel mechanisms with multi-translational DoF. Based on the analysis of the DoF of the end effector, the parametric expressions of a certain point on the end effector can be obtained by coordinate transformation. Through analysis, it proves that a kind of parallel mechanisms with large workspace can be synthesized. Based on the analysis of the DoF of the end effector, it also presents an analytical method for the kinematics and dynamics of spatial parallel mechanisms, in which the whole process is simpler.