This paper deals with the conceptual design and optimal dimensional synthesis of a novel 2-DOF translational parallel robot for pick-and-place operations. In a conceptual design phase, the conditions for generating such kinds of parallel robots are investigated, leading to the invention of a 2-D version of the Delta robot. Combining this robot with a 1-DOF feed mechanism, a hybrid robot can be created which is particularly suitable for transporting objects at very high speed in a plane plus a relatively slow or step-by-step, yet long distance motion, normal to the plane. The kinematic optimality of the 2-DOF translational parallel robot is achieved by minimizing a global and comprehensive conditioning index subject to a set of appropriate constraints. The application of this robot to the development of a device for quality inspection of rechargeable batteries is used to demonstrate its applicability.

Mainly drawing on screw theory and linear algebra, this paper presents a general approach for Jacobian analysis of lower mobility manipulators. Given IntroductionLower mobility manipulators having fewer than six degrees of freedom (DOF) have drawn continuous interest in both industry and academia for many years. Velocity, accuracy and stiffness are three important performance factors that should essentially be considered in design of the lower mobility manipulators, particularly in the many circumstances where high speed, high precision and high rigidity are basic requirements.Mathematically, the common manipulation required for velocity, accuracy and stiffness modeling is to formulate a specific linear map between two vector spaces at a given configuration. For example, velocity modeling involves the linear map between actuator rates and velocity twist of the end-effector. The matrix form of this map is known as the velocity Jacobian or Jacobian, for simplicity [1][2][3]. For accuracy modeling the required linear map is between source errors (inclusive of geometric errors of the components and movement errors of the actuators, for instance) and pose accuracy of the end-effector. In stiffness modeling it becomes the linear map between the deformation twist and the externally-applied wrench imposed on the end-effector. This common feature makes it possible to formulate all these models under a unified mathematical framework.In the last few decades, intensive efforts have been made toward Jacobian analysis, and several useful approaches are now at hand. The most straightforward method is to differentiate a set of vector-based constraint equations. Although Jacobian analysis in an implicit form can easily be carried out for general discussion purposes [4], it is by no means an easy task to achieve general and explicit expressions, as is shown by the case-by-case studies [5-21] though many others may not be included. The screw-based method [1,[22][23][24][25][26][27][28][29] is more powerful and easily gives deep insight into the constraints imposed upon of a robotic system thanks to the compact and meaningful representation. The initial work along this track can be traced back to the original contribution made by Hunt [22]: expressing velocity twist of the end-effector as a linear combination of joint screws leads easily to the Jacobian of 6-DOF parallel manipulators [1,[23][24]28]. By exploiting the reciprocal properties of screw systems within a single open loop kinematic chain, the idea was then extended by Joshi and Tsai to develop a general and systemic approach for Jacobian analysis of non-overconstrained lower mobility parallel manipulators, resulting in a brand new 66 Jacobian known as the overall Jacobian, which accounts for both the actuation and constraint wrenches imposed upon the platform [27]. Use of the overall Jacobian can well explain the constraint singularity problem of a lower mobility parallel manipulator. More recently, the screw-based method has been employed to deal with the inter...

No abstract