Structural Synthesis of Parallel Robots
This is the first book of robotics presenting solutions of uncoupled and fully-isotropic parallel robotic manipulators and a method for their structural synthesis. . The originality of this work resides in combining the new formulae for mobility connectiv
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Kinematics of parallel robots is very important for structural synthesis. We have seen in chapter 2 that the structural parameters of parallel robots are mainly kinematically defined. The duality between velocity and force allows us to give alternative definitions of structural parameters based on statics. The author has preferred the kinematic definition, considering that the kinematic nature of the structural parameters facilitates the understanding of their meaning. Apparently, we are more skilled in imagining the motion than imaging the static or dynamic forces. In this chapter, we will introduce the main models and performance indices used in parallel robots. In general, to study robot motions, geometric and kinematic models are used. We will present the general approach used to set up these models and we emphasize the Jacobian matrix which is the main issue in defining robot kinematics, singularities and performance indices. We saw in chapter 2 that the Jacobian is the matrix of the linear transformation between the velocity joint space and the operational space. This matrix contains very important information concerning robot behavior from a kinematic and static (kinetostatic) point of view. The Jacobian will be used to define and to characterize motion decoupling in parallel robots. In modern design theories, decoupling the functional requirements has become a basic design principle (Suh 1990). In robotics, this principle leads to significant advantages in design, modeling, motion planning and control (Vukobratovic and Kircanski 1983; Konstantinov et al. 1987; Patarinski et al. 1991; Patarinski and Uichiyama 1993; Youcef-Toumi 1992; Galabov et al. 1999). In many robotic applications the possibility of decoupling end-effector motion becomes a cornerstone criterion in the choice of the robot mechanism. The problem is that in the early stage of parallel robot design the Jacobian matrix is not yet known. For structural synthesis of parallel robots we use an alternative method to define motion decoupling and singularities, which does not need prior knowledge of the Jacobian matrix. This method is based on the main structural parameters introduced in chapter 2 via the theory of linear transformation.
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4 Kinematic analysis
4.1. Decoupling in axiomatic design Axiomatic design is a new design theory developed by Suh (1990) to establish a scientific foundation for the design field, and provide a fundamental basis for the creation of products, processes, systems, software and organizations. This is a significant departure from the conventional design processes largely dominated by empiricism and intuition. Axiomatic design considers that the design objective is always stated in the functional domain, whereas the physical solution is always generated in the physical domain. These two domains are in permanent interconnection at every hierarchical level of the design process. To satisfy the design objectives defined in terms of functional requirements (FRs), a physical embodiment defined in terms of design paramet
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