Abstract
Today there is an abundance of kinematic arrangements of parallel mechanisms with different numbers of degrees of freedom available in robotics. The most commonly used are described in this chapter. In contrast to serial mechanisms, universal and spherical joints are common in parallel mechanisms, as the majority of joints in a parallel mechanism robot are passive. The complexity of parallel mechanisms becomes evident in their mathematical analysis. In parallel mechanisms, a closed-form solution to the direct kinematics problem does not, in general, exist. Difficulties are also due to the multiple solutions and to the fact that the existence of a real solution is not always guaranteed.
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Lenarčič, J., Bajd, T., Stanišić, M.M. (2013). Parallel Mechanisms. In: Robot Mechanisms. Intelligent Systems, Control and Automation: Science and Engineering, vol 60. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4522-3_7
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