A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism

Topology and performance are the two main topics dealt in the development of robotic mechanisms.However,it is still a challenge to connect them by integrating the modeling and design process of both parts in a unified frame.As the properties associated with topology and performance,finite motion and instantaneous motion of the robot play key roles in the procedure.On the purpose of providing a fundamental preparation for integrated modeling and design,this paper carries out a review on the existing unified mathematic frameworks for motion description and computation,involving matrix Lie group and Lie algebra,dual quaternion and pure dual quaternion,finite screw and instantaneous screw.Besides the application in robotics,the review of the work from these mathematicians concentrates on the description,composition and intersection operations of the finite and instantaneous motions,especially on the exponential-differential maps which connect the two sides.Furthermore,an in-depth discussion is worked out by investigating the algebraical relationship among these methods and their further progress in integrated robotic development.The presented review offers insightful investigation to the motion description and computation,and therefore would help designers to choose appropriate mathematical tool in the integrated design and modeling and design of mechanisms and robots.

Geometric error analysis of an over-constrained parallel tracking mechanism using the screw theory

This paper deals with geometric error modeling and sensitivity analysis of an overconstrained parallel tracking mechanism. The main contribution is the consideration of overconstrained features that are usually ignored in previous research. The reciprocal property between a motion and a force is applied to tackle this problem in the framework of the screw theory. First of all, a nominal kinematic model of the parallel tracking mechanism is formulated. On this basis, the actual twist of the moving platform is computed through the superposition of the joint twist and geometric errors. The actuation and constrained wrenches of each limb are applied to exclude the joint displacement. After eliminating repeated errors brought by the multiplication of wrenches, a geometric error model of the parallel tracking mechanism is built. Furthermore,two sensitivity indices are defined to select essential geometric errors for future kinematic calibration. Finally, the geometric error model with minimum geometric errors is verified by simulation with SolidWorks software. Two typical poses of the parallel tracking mechanism are selected, and the differences between simulation and calculation results are very small. The results confirm the correctness and accuracy of the geometric error modeling method for over-constrained parallel mechanisms.

Rigid-Soft Coupled Robotic Gripper for Adaptable Grasping

Inspired by the morphology of human fingers,this paper proposes an underactuated rigid-soft coupled robotic gripper whose finger is designed as the combination of a rigid skeleton and a soft tissue.Different from the current grippers who have multi-point contact or line contact with the target objects,the proposed robotic gripper enables surface contact and leads to flexible grasping and robust holding.The actuated mechanism,which is the palm of proposed gripper,is optimized for excellent operability based on a mathematical model.Soft material selection and rigid skeleton structure of fingers are then analyzed through a series of dynamic simulations by RecurDyn and Adams.After above design process including topology analysis,actuated mechanism optimization,soft material selection and rigid skeleton analysis,the rigid-soft coupled robotic gripper is fabricated via 3D printing.Finally,the grasping and holding capabilities are validated by experiments testing the stiffness of a single finger and the impact resistance of the gripper.Experimental results show that the proposed rigid-soft coupled robotic gripper can adapt to objects with different properties(shape,size,weight and softness)and hold them steadily.It confirms the feasibility of the design procedure,as well as the compliant and dexterous grasping capabilities of proposed rigid-soft coupled gripper.