Parallel Manipulators, New Developments

Parallel manipulators are characterized as having closed-loop kinematic chains. Compared to serial manipulators, which have open-ended structure, parallel manipulators have many advantages in terms of accuracy, rigidity and ability to manipulate heavy loads. Therefore, they have been getting many attentions in astronomy to flight simulators and especially in machine-tool industries.The aim of this book is to provide an overview of the state-of-art, to present new ideas, original results and practical experiences in parallel manipulators. This book mainly introduces advanced kinematic and dynamic analysis methods and cutting edge control technologies for parallel manipulators. Even though this book only contains several samples of research activities on parallel manipulators, I believe this book can give an idea to the reader about what has been done in the field recently, and what kind of open problems are in this area. The article has described an innovative spherical parallel wrist developed at the Polytechnic University of Marche in Ancona, revisiting all the main design steps, from kinematic synthesis up to physical prototyping. Machine kinematics has been worked out in closed form and all the singularity surfaces have been analysed: it has been pointed out that the mechanism does not possess inverse kinematics singularities, while direct kinematics singularities and translation singularities lie on the same closed surface. The inner space, where motion paths can be safely planned, has been identified and unfortunately it cannot be enlarged by kinematics optimisation because machine's Jacobian does not depend on geometrical parameters. For this reason, it was decided to drive machine design by dynamic optimisation concepts and an inverse dynamics model has been developed: the study of machine's dynamic manipulability, by means of different algebraic tools, led to the final design of the wrist, that has been also verified with structural analysis packages. The availability of the dynamic model, on the other hand, will be useful for the development of model based control systems, able to exploit the high potentials of direct drive actuation: a first dynamic analysis, moreover, shows that simplified models could be used, since the non-diagonal terms of mass matrix are much smaller than diagonal terms and platform's inertia could be neglected, at least when manipulator is far from singular configurations. All design steps have been performed in a virtual prototyping environment, that allowed to take into consideration simultaneously the constraints of the mechanics and the problems of the controller, allowing to assess the performances of the closed-loop system. The physical prototyping of the machine, however, allowed to validate the good properties envisaged during the design phase but also to experience the disadvantages of the concept itself: they are mainly due to the scarce accessibility of the centre of the spherical motion, which is common to most parallel wrists, and to the difficult assembly, which requires a precise alignment of joints axes: this problem has been partially overcome by the manufacturing of specific fixtures that are characterised by very high accuracy and are used while assembling the machine. The machine has been moved so far only through motors drives and a conventional PID position controller is actually being developed: more advanced control systems, able to exploit the high dynamics of the design and the power of direct actuation, will be studied soon Through either method of obtaining a constrained dimensionally homogeneous Jacobian matrix (proposed by (Gosselin, 1992) or by (Pond & Carretero, 2006)) for planar mechanisms, a choice exists on which of the potential six Cartesian velocity components on the end effector be used to define the task space velocity variables. The choice has an influence on the resulting Jacobian matrix and therefore its condition number and singular values. Without constraining the Jacobian matrix, the condition number was demonstrated to be essentially meaningless, as in (Kim & Ryu, 2003). In terms of measuring dexterity, the constrained dimensionally homogeneous Jacobian matrices (J'P) are superior to the screw based Jacobian matrix (J) in that they are dimensionally consistent. Furthermore, the six matrices (J'P) are superior to the 3? 6 dimensionally homogeneous matrix (J') in that they are constrained, and therefore provide true dexterous information. The condition number and singular values of each of the six matrices (J'P) are different for any given pose. Therefore, dexterity measures involving only one of the six (J'P) matrices are potentially bias. Four potential strategies for dexterity measurement have been proposed based on the condition number and/or singular values of the Jacobian matrices obtained in all six cases. Each measure has a distinct physical meaning, as discussed. In sum, the Jacobian matrix formulation presented in this chapter allows, for the first time, to quantitatively compare different mechanism architectures with complex degrees of freedom in terms of dexterity. Moreover, as illustrated in this chapter, the formulation is not limited to parallel manipulators as it can also be used to quantitatively compare the dexterity of different architectures as long as the end effector is represented by an equivalent set of points. Quantitative dexterity comparisons will allow robot designers to better select proper mechanisms for specific tasks Recent advances in parallel robot architectures encourage related research on kinematic calibration of parallel mechanisms. This paper proposes a novel calibration approach based on observations of manipulator leg parallelism with respect to the Cartesian planes. Presented for the Orthoglide-type mechanisms, this approach may be also applied to other manipulator architectures that admit parallel leg motions (along the Cartesian axes) or, in more general case, allow locating the leg in several postures with a common intersection point. The proposed calibration technique employs a simple and low-cost measuring system composed of standard comparator indicators attached to the universal magnetic stands. They are sequentially used for measuring the deviation of the relevant leg location while the manipulator moves the tool-center-point in the directions x, y and z. From the measured differences, the calibration algorithm estimates the joint offsets and link lengths that are treated as the most essential parameters that are difficult to identify by other methods. The presented theoretical derivations deal with the sensitivity analysis of the proposed measurement method and also with the calibration accuracy. The validity of the proposed approach and efficiency of the developed numerical algorithm were confirmed by the calibration experiments with the Orthoglide prototype, which allowed dividing the residual root-mean-square by three. To increase the calibration precision, future work will focus on the development of the specific assembling fixture ensuring proper location of the linear actuators and also on the expanding the set of the identified model parameters and compensation of the nongeometric errors that are not identified within the frames of the adopted model