Type synthesis and kinematics of general and analytic parallel mechanisms

Parallel mechanisms (PMs) have been and are being put into more and more use in motion simulators, parallel manipulators and parallel kinematic machines. To meet the needs for new, low-cost and simple PMs, a systematic study on the type synthesis and kinematics of general PMs and analytic PMs (APMs) is performed in this thesis. An APM is a PM for which the forward displacement analysis (FDA) can be solved using a univariate polynomial of degree 4 or lower. Firstly, a general approach is proposed to the type synthesis of PMs based on screw theory. Types of PMs generating 3-DOF translations, spherical motion and 4-DOF (3 translations and 1 rotation) motion are obtained. Full-cycle mobility conditions and validity conditions of the actuated joints are derived for these cases. Secondly, several approaches are proposed for the type synthesis of APMs. One class of the newly obtained APMs is linear PMs generating 3-DOF translations for which the FDA can be obtained by solving a set of linear equations. Thirdly, we present a comprehensive study, including the type synthesis, kinematic analysis and kinematic synthesis, on LTPMs. An LTPM is a PM generating 3-DOF translations with linear input-output equations and without constraint singularities. The proposed LTPMs may or may not contain some inactive joints and/or redundant joints. It is proved that an LTPM is free of uncertainty singularity. Isotropic conditions for the LTPMs are also revealed. An isotropic LTPM is globally isotropic. Fourthly, the FDA of several APMs is dealt with and the maximum number of real solutions is revealed for certain APMs. Finally, the singularity analysis of several typical PMs is dealt with. The one-to-one correspondence between the analytic expressions for four solutions to the FDA and the four singularity-free regions is revealed for a class of analytic planar PMs. This further simplifies the FDA since one can obtain directly the only solution to the FDA once the singularity-free region in which the PM works is specified. The singularity analysis of a class of PMs is simplified based on the instability analysis of structures. The geometric characteristic is also revealed using linear algebra.