The prime objective of this work is to deal with the kinematics of spatial hybrid manipulators. In this direction, in 1955, Denavit and Hartenberg proposed a consistent and concise method, known as D-H parameters method, to deal with kinematics of open serial chains. From literature review, it is found that D-H parameter method is widely used to model manipulators consisting of lower pairs. However, the method leads to ambiguities when applied to closed-loop, tree-like and hybrid manipulators. Furthermore, in the dearth of any direct method to model closed-loop, tree-like and hybrid manipulators, revisions of this method have been proposed from time-to-time by different researchers. One such kind of revision using the concept of dummy frames has successfully been proposed and implemented by the authors on spatial hybrid manipulators. In that work, authors have addressed the orientational inconsistency of the D-H parameter method, restricted to body-attached frames only. In the current work, the condition of body-attached frames is relaxed and spatial frame attachment is considered to derive the kinematic model of a 7-degree of freedom spatial hybrid robotic arm, along with the development of closed-loop constraints. The validation of the new kinematic model has been performed with the help of a prototype of this 7-degree of freedom arm, which is being developed at Council of Scientific & Industrial Research–Central Scientific Instruments Organisation Chandigarh to aid the surgeon during a medical surgical task. Furthermore, the developed kinematic model is used to develop the first column of the Jacobian matrix, which helps in providing the estimate of the tip velocity of the 7-degree of freedom manipulator when the first joint velocity is known.
Properties of surface Landau–de Gennes Q-tensor models
