## Abstract

Screw theory was proposed by Sir Robert Ball towards the end of the nineteenth century but laid dormant until the work of Brand in 1947. Then Dimentberg in 1965 and Philips and Hunt in 1967 illustrated the elegance of this theory in spatial kinematics. Hunt in particular used the theory of screws to reveal geometrical insight into the analysis of closed kinematic chains and spatial mechanisms. The duality of statics and kinematics offered by screw theory has opened a new horizon in parallel robot design as researchers recur to this mathematical tool for the calculation of the instantaneous kinematics and the determination of the mobility of a given robotic architecture. This chapter presents the mobility analysis of two families of 3-DOF parallel manipulators using screw theory. The first family consists of the 2R1T 3-PSP, 3-PPS, 3-PCU, and a new 3-CUP parallel manipulator, while the second family is formed by the fully translational 3-RPC-Y, 3-RCC, and the novel 3-RPC-T parallel mechanism. The analysis obtains the branch motion-screws for the abovementioned architectures and determines the sets of platform constraint-screws. The mobility of each manipulator platform is thus obtained by determining the reciprocal screws to the platform constraint-screw sets and the platforms are identified to have three instantaneous independent degrees of freedom which are: (i) a translation along an axis perpendicular to the base; and (ii) two rotations about two skew axes for the first family of manipulators, while the second family has fully translational mobility. The mobility analysis performed in this chapter is validated using motion simulations.

Original language | English |
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Title of host publication | Robotics: State of the Art and Future Trends |

Publisher | Nova Science Publishers Inc |

Pages | 75-111 |

Number of pages | 37 |

ISBN (Print) | 9781621004035 |

Publication status | Published - Jan 2013 |