Direct kinematics with analytic solutions is critical to the real-time control of parallel mechanisms. Therefore, the type synthesis of a mechanism having explicit form of forward kinematics has become a topic of interest. Based on this purpose, this paper deals with the type synthesis of 1T2R parallel mechanisms by investigating the topological structure coupling-reducing of the 3UPS&UP parallel mechanism. With the aid of the theory of mechanism topology, the analysis of the topological characteristics of the 3UPS&UP parallel mechanism is presented, which shows that there are highly coupled motions and constraints amongst the limbs of the mechanism. Three methods for structure coupling-reducing of the 3UPS&UP parallel mechanism are proposed, resulting in eight new types of 1T2R parallel mechanisms with one or zero coupling degree. One obtained parallel mechanism is taken as an example to demonstrate that a mechanism with zero coupling degree has an explicit form for forward kinematics. The process of type synthesis is in the order of permutation and combination; therefore, there are no omissions. This method is also applicable to other configurations, and novel topological structures having simple forward kinematics can be obtained from an original mechanism via this method.
Purpose -Cosserat continuum models are motivated by modeling size effects in materials with microstructure. While elastic Cosserat continuum models can reproduce size effects in deformation stiffness, inelastic models are often used to capture localization and post failure behavior of materials. In application of inelastic Cosserat models, parameter determination is a difficult issue not fully addressed. The purpose of this paper is to discuss parameter-related characteristic lengths in Cosserat continuum modeling of granular materials. Design/methodology/approach -Based on a Cosserat continuum extension of a hypoplastic model for granular media, interpretation of additional parameters are sought through analysis of simple onedimensional shear. Governing equations are obtained, respectively, for small strain shear formation and for stead flow state in localized zone. Findings -Two characteristic lengths are obtained analytically for granular materials: one governs the size effect near boundaries in shear deformation, the other scales the thickness of shear band in failure. While both characteristic lengths are proportional to the micro-structure length (the mean grain diameter), the former is related to the micro-stiffness parameter, and the latter depends on the microstrength parameter. The results reveal a connection between size effects, the micro-structure length and the material properties. The work also provides a new perspective to inelastic Cosserat continuum models, as well as a possible way for determination micro-deformation and strength parameters. Originality/value -The results reveal a connection between size effects, the micro-structure length and the material properties. The work provides a new perspective and an interpretation to the microdeformation and strength parameters of inelastic Cosserat continuum models, as well as a possible way for determination of these parameters.
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