Daxing Zeng

Over-constraints and a unified mobility method for general spatial mechanisms Part 2: Application of the principle

The pre-research on mobility analysis presented a unified-mobility formula and a methodology based on reciprocal screw theory by HUANG, which focused on classical and modern parallel mechanisms. However its range of application needs to further extend to general multi-loop spatial mechanism. This kind of mechanism is not only more complex in structure but also with strong motion coupling among loops, making the mobility analysis even more complicated, and the relevant research has long been ignored. It is focused on how to apply the new principle for general spatial mechanism to those various multi-loop spatial mechanisms, and some new meaningful knowledge is further found. Several typical examples of the general multi-loop spatial mechanisms with motion couple even strong motion couple are considered. These spatial mechanisms include different closing way: over-constraint appearing in rigid closure, in movable closure, and in dynamic closure as well; these examples also include two different new methods to solve this kind of issue: the way to recognize over-constraints by analyzing relative movement between two connected links and by constructing a virtual loop to recognize over-constraints. In addition, over-constraint determination tabulation is brought to analyze the motion couple. The researches above are all based upon the screw theory. All these multi-loop spatial mechanisms with different kinds of structures can completely be solved by following the directions and examples, and the new mobility theory based on the screw theory is also proved to be valid. This study not only enriches and develops the theory and makes the theory more universal, but also has a special meaning for innovation in mechanical engineering.

Performance Analysis and Optimal Design of a 3-DOF 3-PRUR Parallel Mechanism

In this paper, a 3-DOF 3-PRUR parallel mechanism (PM) is chosen for performance analysis and optimal design. First, the mobility of the PM is analyzed by using screw theory. Then, the kinematics of this PM is studied based on the geometrical characteristics and the Jacobian matrix is derived. Furthermore, we research some performance indices with respect to the Jacobian matrix over the whole workspace and nondimensional parameters when the input is given, and their performance atlases are obtained with different inputs. Finally, the optimal design of the PM is determined according to the performance atlases, and some examples are presented.

Biomimetic Shoulder Complex Based on 3-PSS/S Spherical Parallel Mechanism

The application of the parallel mechanism is still limited in the humanoid robot fields, and the existing parallel humanoid robot joint has not yet been reflected the characteristics of the parallel mechanism completely, also failed to solve the problem, such as small workspace, effectively. From the structural and functional bionic point of view, a three degrees of freedom(DOFs) spherical parallel mechanism for the shoulder complex of the humanoid robot is presented. According to the structure and kinetic characteristics analysis of the human shoulder complex, 3-PSS/S(P for prismatic pair, S for spherical pair) is chosen as the original configuration for the shouder complex. Using genetic algorithm, the optimization of the 3-PSS/S spherical parallel mechanism is performed, and the orientation workspace of the prototype mechanism is enlarged obviously. Combining the practical structure characteristics of the human shouder complex, an offset output mode, which means the output rod of the mechanism turn to any direction at the point a certain distance from the rotation center of the mechanism, is put forward, which provide possibility for the consistent of the workspace of the mechanism and the actual motion space of the human body shoulder joint. The relationship of the attitude angles between different coordinate system is derived, which establishs the foundation for the motion descriptions under different conditions and control development. The 3-PSS/S spherical parallel mechanism is proposed for the shoulder complex, and the consistence of the workspace of the mechanism and the human shoulder complex is realized by the stuctural parameter optimization and the offset output design.

A Family of Novel 2 DOF Rotational Decoupled Parallel Mechanisms

This paper presents a family of novel 2 degree of freedom (DOF) rotational decoupled parallel mechanisms(DPMs). The basic feature of this family is that the moving platform and the fixed base of the DPMs are connected by three limbs, also the motion of the moving platform is decoupled, besides the first and second limbs structure a four-bar linkage or guide bar mechanism. Then we take the UPRUSPS DPM as an example and use the constraint screw method to analyze the motion feature of this DPM. The mobility of the DPM has also been calculated by the Modified Grubler-Kutzbach criterion. At last, the kinematics and decoupled feature of this DPM is analyzed. All the DPMs in this paper are simple and no complicated computation is required for real-time control. So these novel DPMs have very good application value for tracking equipments, such as radar, missile etc. As far as we are aware, this paper puts forward 2 DOF rotational DPMs with three limbs for the first time.

Over-constraint and a unified mobility method for general spatial mechanisms part 1: Essential principle

Compared with the parallel mechanisms, the mobility analysis of the general multi-loop spatial mechanisms(GMSMs) is more difficult to obtain correct results. The reason is that its multi-loop is formed through several times of closings and there also exists motion coupling even strong coupling, where the over-constraints are concealed. However, the mobility analysis for this kind of mechanisms has been paid few attentions. A new systemic methodology for analyzing mobility is proposed for GMSMs also based on the screw theory. The key issue for mobility analysis is to recognize the over-constraint. Firstly, three theorems are given and point out: the reason and site of over-constraint occurrence, calculating the number of over-constraints by the screw theory, and how to analyze the over-constraints for a single-loop mechanism as well. Then, three closing forms for GMSMs are proposed including rigid closure, movable closure and dynamic closure, and for the three different forms the different analysis methods are also given. Especially, for the most difficult issue of GMSMs with the multi-loop closure in many times and the inevitable motion coupling, two important methods are proposed: “recognizing over-constraints by analyzing relative movement” and “recognizing over-constraints by virtual loop”. The two methods are well used to solve the issue. Above-mentioned principles are not only systematic and effective but also unified. They provide a theoretical basis for the general multi-loop spatial mechanisms.

Novel mobility formula for parallel mechanisms expressed with mobility of general link group

The determination of virtual constraints is always one of the key and difficult problems in traditional mobility calculation. To make mobility calculation simple, considering avoiding virtual constraints, some new formulae have been presented, however these formulae can hardly intuitively reflect general link group’s restrictions on output member and its influences on independence of output parameters, which is premise to the judgment of the properties of mobility. Towards the problem to reveal the intrinsic relationship between the degree of freedom(DOF) of a mechanism, the link group, and the dimension of output parameters, also to avoid determination of virtual constraint, based on the new concepts of the “DOF of general link group” and “node parameters”, a new formula in the calculation of the mobility of mechanisms is presented that is expressed with DOFs of the general link groups and rank of motion parameters of base point of the output link. It is named GOM(mobility of groups and output parameter) formula. On the basis of new concepts of “effective parameters” and “invalid parameters”, a rule is put forward for solving the DOF of mechanisms with invalid parameters by GOM formula, that is, the base point parameters are the subset of effective parameters of link group. Thereafter, several examples are enumerated and the results coincide with the prototype data, which proves the validity of the proposed formula. Meanwhile, it is obtained that the necessary and sufficient condition for the judgment of output parameters independence is that each of the DOF of the link group is not less than zero. The proposed formula which is simple in calculation provides theoretical basis for the judgment of independence of output parameters and provides references for type synthesis of novel parallel mechanisms with independence requirements of their output parameters.

The Screw Motion Simulation on 3-RPS Parallel Pyramid Mechanism

In this paper, a 3-RPS pyramid mechanism is analysed. Three constraining force screw limit the translations of the pyramid in three directions, only three rotating freedom is allowed in spatial. The mechanism has screw motion along its diagonal. The input rationality of the mechanism is discussed using the screw theory. We build up the model of this mechanism with the application of MATLAB, study the simulation of the screw movement, get a series of movement curves and verify the theories analysis by the numerical example.

Dynamic Response and Stability Analysis of a Parallel Mechanism with Clearance in Revolute Joint

The clearances in kinematic pair are inevitable, which will affect the accuracy and stability of the mechanism directly. A two rotational decoupled parallel mechanism RU-RPR is taken as the research object. Considering the clearance existing in the revolute pair, the dynamics equations are established. Then the effects of clearance on the dynamic characteristics of the mechanism are researched. Meanwhile, a spring is added to the mechanism, and its influences on the dynamic of the mechanism are analyzed. In order to further improve the dynamic response of the mechanism, the genetic algorithm is applied to optimize the related parameters of the spring. The research contents possess theoretical guidance significance on improvement of the dynamic characteristics and control of the chaotic motion of the parallel mechanism with clearances.

Mechanics unloading analysis and experimentation of a new type of parallel biomimetic shoulder complex

The structure design for high ratio of carrying capacity to deadweight is one of the challenges for the bionic mechanism, while the problem concerning high carrying capacity has not yet be solved for the existing shoulder complex. A new type biomimetic shoulder complex, which adopts 3-PSS/S(P for prismatic pair, S for spherical pair) spherical parallel mechanism (SPM), is proposed. The static equilibrium equations of each component are established by using the vector method and the equations for constrain forces with certain load are solved. Then the constrain force on the middle limb and that on the side limbs are compared in order to verify the unloading performance of the mechanism. In addition, the prototype mechanism of the shoulder complex is developed, and the force feedback experiment is conducted to verify the static analysis, which indicates that the middle limb suffers most of the external force and the effect of mechanics unloading is achieved. The 3-PSS/S spherical parallel mechanism is presented for the shoulder complex, and the realization of mechanics unloading is benefit for the improvement of the carrying capacity of the shoulder complex.

Determination of overconstraint and mobility analysis for planar mechanisms

The mobility(or degree of freedom) analysis of planar mechanisms is traditionally calculated using the Grübler–Kutzbach formula. However, this method often fails in practice due to overconstraint, which is a core problem in all mobility analysis. Analyzing the cause of overconstraint, it is presented that overconstraint in closed-loop mechanisms can be recognized by analyzing the relative movements of the two elements in a rigidity re-closure. A solution to determine the overconstraint in multiloop mechanisms is also proposed. In this method, each loop is opened and the overconstraint can be calculated when the loop is reclosed. A mobility analysis must begin by determining the overconstraint. However, given that most planar mechanisms do not have any overconstraint, it is important to identify rapidly whether overconstraint exists in a mechanism. This paper proposes a concise technique to determine the existence of overconstraint based on the concept of “Assur groups”. To simplify the process of mobility analysis, three new concepts and four relevant theories are introduced. In this paper, the proposed methodology is applied to several types of planar mechanisms, producing results in accordance with the prototype. This shows that the proposed methodology makes performing the mobility analysis of planar mechanisms, including complicated planar mechanisms, accurate, convenient, and fast.