Abstract
In the process of parallel mechanism design, it is difficult to avoid the singularity, especially in the mobile parallel mechanism. Therefore, a new mathematical method to study the singularity of multimode mobile parallel mechanism is proposed. In this paper, the singularity of 3-RSR parallel mechanism (PM) is analyzed by using reciprocal screw methods and linear geometry theory from two aspects of fixed mode and all-attitude multiple motion modes. Specifically, the complete Jacobian matrix of the PM is obtained by using the screw theory, and the reciprocal screw of each branch is expressed with algebraic method and geometric drawing method. Furthermore, the singularity of the PM can be obtained by analyzing the reciprocal screw correlation and using the spatial linear geometry theory. Finally, we analyze the singular configuration of the PM under various modes, which provide theoretical guidance for the gait planning of the multimode mobile PM and will be useful for the selection of mechanism drive and time-sharing control.
Highlights
Parallel mechanisms with high load bearing capacity and precision have been widely used in processing and manufacturing, testing, logistics, and many other applications [1]
In the process of mechanism design, many scholars have proposed a variety of methods to study singular configurations in [9,10,11,12,13,14,15,16,17] and tried to avoid singular configurations [18], but most of these methods use the calculation method to determine whether the value of the Jacobian matrix determinant is zero, or whether the Jacobian matrix is downgraded to judge whether the mechanism is singular
In the design of mobile mechanisms and mobile robots, we make full use of kinematic relationship between the parallel mechanism platforms and the branch chains and combine the idea of multiple operating modes of the parallel platform [23, 24] to integrate multiple motion modes [25] on a mobile parallel mechanism and let the branch chains and platforms participate in rolling, walking, self-traversing, and so on
Summary
Parallel mechanisms with high load bearing capacity and precision have been widely used in processing and manufacturing, testing, logistics, and many other applications [1]. We proposed a new mathematical method to study the singularity of parallel mechanism. The driving control choices and avoidance of singularities in realizing these motion modes are unclear. This paper analyzes the singularity of 3-RSR multimode mobile parallel mechanism by means of the reciprocal screw theory and the spatial geometric theory from two points of view: the fixed mode and the all-attitude multiple motion modes, and the driving selection and control of mechanism in the moving mode are further studied.
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