Finite and Instantaneous Screw Theory in Robotic Mechanism

mathematical ones. The instantaneous screw can be directly used to describe velocities, forces, powers, and analyze performances of various robotic mechanisms including open-loop and closed-loop mechanisms as well as hybrid ones. Taking the orders of mechanisms with different DoFs into account, the classification of screw systems which are vector spaces spanned by no more than six screws was carried out by Gibson and Hunt, Martínez and Duffy [37], Dai and Jones [38]. They presented a comprehensive enumeration of possible linear combinations of given instantaneous screws that are central to the analysis of multi-DoF mechanisms and established normal form for each screw system in terms of base screws. Based upon these work, Huang [39], Dai [40], and their colleagues implemented mobility analysis of numerous mechanisms through determining the orders and characteristics of mechanisms’ instantaneous screw systems and corresponding reciprocal systems. By employing instantaneous screw systems and their reciprocal products to describe instantaneous motions of a multi-closed-loop mechanism, its limbs, joints and their relationships, type synthesis of multi-closed-loop mechanisms was carried out in an instantaneous motion level by Huang and Li [41, 42], Fang and Tsai [43, 44], Kong and Gosselin [45, 46], as well as the authors of this book [47–53]. This is actually the reverse process of mobility analysis. As for any given robotic mechanism, the velocity, force, stiffness, accuracy, acceleration, and dynamic modeling and performance evaluation can be done using the instantaneous screw based Jacobian matrices or Hessian matrices. In this way, performance analysis, optimal design, and kinematic calibration of different categories of mechanisms can be carried out.