Mobility Analysis Of Parallel Mechanisms Research Articles

A machine learning-based approach for automatic motion/constraint and mobility analysis of parallel robots

Abstract Motion and constraint identification are the fundamental issue throughout the development of parallel mechanisms. Aiming at meaningful result with heuristic and visualizable process, this paper proposes a machine learning-based method for motions and constraints modeling and further develops the automatic software for mobility analysis. As a preliminary, topology of parallel mechanism is characterized by recognizable symbols and mapped to the motion of component limb through programming algorithm. A predictive model for motion and constraint with their nature meanings is constructed based on neural network. An increase in accuracy is obtained by the novel loss function, which combines the errors of network and physical equation. Based on the predictive model, an automatic framework for mobility analysis of parallel mechanisms is constructed. A software is developed with WebGL interface, providing the result of mobility analysis as well as the visualizing process particularly. Finally, five typical parallel mechanisms are taken as examples to verify the approach and its software. The method facilitates to attain motion/constraint and mobility of parallel mechanisms with both numerical and geometric features.

Twist and finite twist analysis of 2UPR-SPR parallel mechanism based upon screw theory

This paper discusses the issue on mobility analysis of parallel mechanism. The analysis is focused on the two-rotational and one-translational 2UPR-SPR parallel mechanism which has interesting motion properties that one rotation of this mechanism has fixed direction, while the other rotation and the translation have variable directions. Twist analysis is conducted to obtain the feasible velocities of the moving platform at any configuration of the mechanism, and finite twist analysis is carried out to obtain the feasible displacements of the moving platform when the mechanism moves away from the initial configuration to any configuration. The obtained parametric velocity space at any configuration and parametric displacement manifold from the initial configuration to any configuration are formulated, which are proved to contain the same motion information and have the same effect in mobility analysis. Through analyzing the 2UPR-SPR mechanism, it is revealed that both twist and finite twist are effective to describe continuous motions of rigid body or mechanism. This enriches the relation between twist and finite twist, and unifies the applications of these two kinds of screws in mobility analysis.

Instantaneous mobility analysis using the twist space intersection approach for parallel mechanisms

This paper focuses on instantaneous mobility analysis of parallel mechanisms using the twist space intersection approach. In this study, a nullspace-associated approach is first presented to determining the intersection of screw systems based on screw theory and linear algebra. The approach provides a way of investigating the motion-screw system of the platform for parallel mechanisms without constraint analysis. By investigating the order of the motion-screw system of a platform, this paper presents the instantaneous mobility of a 3-revolute-prismatic-spherical (3-RPS) parallel mechanism, that of a Bennett mechanism, that of a revolute-cylindrical-prismatic-prismatic (RCPP) mechanism and that of a 3-prismatic-universal-prismatic (3-PUP) parallel mechanism. This way of examining the mobility is equivalent to the way based on constraint analysis, presenting the validity of the presented approach and the correctness of instantaneous mobility analysis using the twist space intersection approach for parallel mechanisms and for overconstrained mechanisms.

Computer-aided mobility analysis of parallel mechanisms

To determine mobility properties is one of the most challenging issue in the analysis and synthesis of parallel manipulators (PMs). However, currently, the most used methods mainly rely on experiences and manual analysis, which led to inefficient implementation. The motivation of this paper is to present an automatic mobility analysis algorithm and software package for the researchers and designers with an effective and practical means. According to the topological design theory of PMs based on position and orientation characteristic (POC) equations, this paper proposes a set of computer algorithmic rules and procedures for automated mobility analysis of PMs in the most user-friendly and efficient way. Firstly, a complete digital information model for topological structures which has a mapping relationship with the POC of a PM is proposed. This model not only describes the dimension of the motion outputs, but also includes the mapping relationship between the output orientation and the axes of the kinematic joints. Secondly, algorithmic rules are established that convert the union and intersection operations of POC into binary logical operations and then the detailed algorithmic procedures for an automatic mobility analysis are presented. In what follows, a corresponding software for automatic mobility analysis is described. The software package is equipped with a GUI that facilitates the input and allows the visualization of the results. Finally, four typical examples are provided to show the effectiveness of the software package for most of parallel mechanisms (not including some paradoxical mechanisms).

Mobility analysis of parallel mechanisms based on screw theory and mechanism topology

A practical method for mobility analysis of mechanisms is presented in this article, which is based on the screw theory and the topology structure of mechanisms. The proposed method can be summarized as one core principle and two key techniques. The core principle is that the series connection of kinematic pairs is equivalent to the superposition of corresponding degrees of freedom, and the parallel connection of kinematic pairs is equivalent to the superposition of corresponding constraints. The first key technique for analyzing the mobility of mechanisms is to correctly identify the series and parallel connection relationship between all kinematic pairs, that is, the mechanism topology structure. Another key technique is transforming the screws and reciprocal screws from local coordinate systems to the global coordinate system. First, the above-mentioned method is presented in theory. Then, several examples are analyzed using it, which validate its effectiveness and universality.

A visual graphic approach for mobility analysis of parallel mechanisms

A visual graphic approach for mobility analysis of parallel mechanisms

Mobility Bifurcation of Two 1R3T Parallel Mechanisms Based on Lie Group

Mobility bifurcation of 1R3T (R—rotational,T—translational) parallel mechanisms is studied by applying Lie group theory. Some theoretical fundamentals necessary for application of Lie group theory to mobility analysis of parallel mechanisms are briefly reviewed. Mobility analysis of the 2-xPyRyRxRxR/yPxRxRyRyR and 2-xPyRuPxRxR/yPxRvPyRyR parallel mechanisms is performed. It is proved that the two parallel mechanisms have mobility bifurcation with displacement set of the moving platform being {X(x)}∪ {X(y)}. Further,it is obtained that the limb displacement manifold of the 1R3T parallel mechanism with mobility bifurcation is {G(x)}{G(y)} or {X(x)}{R(N,y)}. The structural geometrical conditions of the 1R3T parallel mechanism with mobility bifurcation are also presented. When the moving platform is parallel to the base,the parallel mechanism is in a singular configuration and the moving platform has five instantaneous degrees of freedom. The mobility bifurcation happening in this singular configuration requires five actuators to control the motion of the moving platform.

Mobility Analysis of a Novel 3-5R Parallel Mechanism Family

Mobility analysis of a novel 3-5R parallel mechanism family whose limb consists of a 2R and a 3R parallel subchain is performed by the aid of screw theory. A mobility criterion applicable to such 3-leg parallel mechanisms in which each kinematic chain contains five kinematic pairs is proposed. It is shown that under different structural conditions, the 3-5R parallel mechanism can have 3, 4, or 5 DOF (degrees of freedom). The structural conditions that guarantee the full-cycle mobility are analyzed. The analysis and the method presented in this paper will be helpful in using such a 3-5R parallel mechanism family and introduce new insights into the mobility analysis of parallel mechanisms.