| Due to the fact that the rotational motion is relative to both the direction and location of the revolute axis, the design of parallel mechanisms (PMs) with rotational degrees of freedom (DOFs) is more complex than the design of PMs only with translational DOFs. Therefore, the design of PMs with rotational DOFs, especially with multi-rotational DOFs, is always one focus of the structural synthesis of mechanism design. In consideration of the existing problems that the PMs with multi-rotational DOFs confront in real application, the research of this contribution will be carried out in two directions:one direction towards studying PMs with high rotational capability, and the other direction towards studying PMs with the behavior of virtual center of motion (VCM).To address the problem that general PMs suffer from the disadvantage of limited rotational angles caused by the interference between limbs and the moving platform, the concept of designing new non-rigid moving platforms is proposed to enhance the rotational capability of PMs. For this purpose, the general topology graph of PMs with a non-rigid moving platform is proposed, and then the corresponding methodology of structural synthesis is established based on Lie group theory. By means of the proposed methodology of structural synthesis, a series of PMs with a helical joint are synthesized which have the high rotational capability about two or three axes.One new non-rigid moving platform with two rotational DOFs is proposed. Based on the concept of partially decoupled kinematics and the proposed methodology of structural synthesis, a series of PMs with two rotational and three translational (2R3T) DOFs or two rotational and two translational (2R2T) DOFs are presented. To deal with the problem that the arrangement of four limbs adopted by the 2R3T PMs brings about, the use of five-bar planar mechanism is suggested to actuate the two joints of one limb close to the base. Then the kinematics and workspace of one of the synthesized 2R3T PMs are presented. Through the analyses of singularity and interference, the results prove that by means of actuation redundancy, the studied 2R3T PM indeed possesses the high rotational capability about two axes, and is suitable for the application of parallel machine tools or multi-axis 3D printing.Two classes of non-rigid moving platforms with three rotational DOFs are proposed. By means of the similar method, two classes of PMs with 3R3T DOFs or 3R2T DOFs are presented. Then take one 3R3T PM of each class as examples to illustrate the approach of analyzing the kinematic problems of PMs with a non-rigid moving platform on the basis of screw theory in detail. Meanwhile, the singular configurations belonging to inverse/direct kinematic singularity, constraint singularity and twist singularity, respectively, are discussed by virtue of screw theory and Lie group theory. Through concluding the analyses about the velocity relation and singularity, an approach to derive the Jacobian matrices of PMs with a non-rigid platform is established based on the concept of transmission wrenches. The numerical analysis is implemented as well. The result shows that resorting to actuation redundancy, the proposed PMs can continuously rotate about three axes up to large angles with no interference and singularity, which also means that the proposed PMs are competent for the application of complicated handling and assembly, or pick and place tasks.To satisfy the requirements of the application of medical ultrasound imaging, a new 6-DOF hybrid mechanism is proposed. By use of the equivalent spherical joint including parallelogram mechanisms, the PMs with a helical joint synthesized above can be entitled with the virtue center of motion. To overcome the disadvantages of the existing ankle rehabilitation devices, a series of new VCM PMs with three rotational DOFs are proposed. In comparison with some multi-degree-of-freedom parallel rehabilitation devices, the proposed PMs can ensure that the mechanism center of rotations matches the ankle axes of rotations. According to the characteristics of ankle rehabilitation, a new scheme of actuation redundancy is presented. Then the kinematic problems for three of the proposed VCM PMs are analyzed, and the variations of performances involving dexterity, singularity, stiffness and dynamics between the redundant PMs and the non-redundant PMs are mainly focused on. The result shows that actuation redundancy is necessary and effective to guarantee the proposed PMs possess sound kinematic and dynamic performances.To deal with the dimensional synthesis of the proposed VCM PMs, a methodology of multi-objective optimization based on Pareto concepts is presented. The general model and solving method about multi-objective problems are introduced first. Based on the problems of the existing multi-objective Differential Evolution (DE) algorithms, a new modified multi-objective DE algorithm is proposed. The dimensional synthesis of one VCM PM for ankle rehabilitation is formulated as a nonlinear constrained multi-objective optimization problem, which includes four objective functions, separately reflecting occupied space, input/output transmission and torque performances, and multi-criteria constraints, such as dimension, interference, kinematics and workspace. To cope with the actuation redundancy of the VCM PM, a new output transmission index is defined. Meanwhile, a special penalty method is presented to tackle the multi-criteria constraints of the VCM PM. Finally, numerical experiments for different optimization algorithms are implemented, and the optimal solutions about the multi-objective model are obtained. The computation results also show that the modified DE algorithm is superior to the other tested algorithms, in terms of the ability of global search and the number of non-dominated solutions. By use of one group of architectural parameters form the computation results, the prototype of the VCM PM for ankle rehabilitation is constructed, and then the preliminary experiment is carried out. The experiment result shows that the prototype can achieve the expected movements of ankle joint. |
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