Type Synthesis Of Parallel Mechanisms Based Upon Finite Screw Theory

This dissertation deals with type synthesis of lower mobility parallel mechanisms using finite screws in quasi-vector form with particular interests in the fundamentals of finite screw theory,the development of a general process for type synthesis,and its application to three families of parallel mechanisms.The following contributions have been made.Having derived a finite screw in quasi-vector form from a dual quaternion,it shows that finite screw in this form is a non-redundant minimal description of rigid body motion.Such a form is particularly useful for analytical operation of finite motion composition.After vigorous proofs of the associativity and derivative laws of screw triangle products,the algebraic structures of the entire set of finite and instantaneous screws are revealed.It shows that the former forms a Lie group under screw triangle product,whereas the latter forms the corresponding Lie algebra under the screw cross product.This important finding bridges the gap linking instantaneous and finite motions in vector forms,allowing type synthesis and parametric modeling of parallel mechanisms to be unified under the umbrella of screw theory.Based upon finite screw representation,a general and systematic approach for type synthesis of parallel mechanisms is proposed.The finite screws of the output link,the limbs and the joints of a parallel mechanism are developed and closely connected.Use of the properties of screw triangle product enables a hierarchical method to be proposed for type synthesis of parallel mechanisms.The method can be implemented by three steps:(1)generating the standard forms of limbs,(2)deriving the derivative forms of limbs by means of substitutions of joint axis locations and joint types;and(3)formulating the assembly conditions.The proposed method naturally ensures the full cycle motions of the synthesized limbs,and enables type synthesis to be implemented in an algebraic manner,a process that cannot be realized by the existing methods.Building upon the finite screw method,type synthesis of three-DOF translational parallel mechanisms is investigated.With the standard limb structures at hand by adding rotational factors in a limb,it shows that all feasible limb structures can be obtained either by replacing the prismatic joints by up to three revolute joints,or by changing sequences of prismatic joints,or by the both.The assembly conditions and actuation arrangements are also developed accordingly,leading to a family of the parallel mechanisms having decoupled translational motions.As a counterpart of three-DOF translational parallel mechanisms,type synthesis of three-DOF spherical parallel mechanisms is studied.Equipped with the standard limb structures developed in the similar way,it shows that the derivative limb structures can be generated by changing the joint positions arbitrarily though the motions they produce are not equivalent to those generated by the standard limb structures.Then,the assembly conditions are achieved using the requirements that no intersections are allowed amongst the different kinds of translations along fixed directions or circles.This leads to a family of spherical parallel mechanisms having symmetrical architectures.Having developed the axode equation of a 4R spherical mechanism using screw triangle product,a new motion pattern is proposed,featuring three independent translations plus a rotation with variable axis,resulting in all feasible limb structures obtained by the same technique addressed above.Then,the assembly conditions are formulated using the axode equation,leading to numerous parallel mechanisms having identical limbs.The outcomes of this dissertation provide an analytical and concise way for type synthesis of lower mobility parallel mechanisms.