There exist some mechanisms with variable topologies that have interesting applications, for examples, legged walking machines, mechanical push-button stopper locks, and various toys. A variable kinematic joint is a kinematic joint that is capable of topological variation in a mechanism with variable topology. This work aims at the topological representations and characteristic analysis of variable kinematic joints. During the operation process of a mechanism, the topology states of a variable kinematic joint can be expressed symbolically as the joint sequences, graphically the digraphs, and mathematically the matrices. With the applications of graph theory, it proves that the topological characteristics of variable kinematic joints appeared with the abilities of reversibility, continuity, variability of degrees of freedom, joint homomorphism, contractibility, and expansibility. Two examples are provided for illustrating how the proposed concepts can be used to analyze and synthesize the variable joints. The results of this work provide a logical foundation for the systematic structural synthesis regarding the kinematic joints and mechanisms with variable topologies.

A crucial design challenge in minimally invasive surgical (MIS) robots is the provision of a fully decoupled four degrees-of-freedom (4-DOF) remote center-of-motion (RCM) for surgical instruments. In this paper, we present a new parallel manipulator that can generate a 4-DOF RCM over its end-effector and these four DOFs are fully decoupled, i.e., each of them can be independently controlled by one corresponding actuated joint. First, we revisit the remote center-of-motion for MIS robots and introduce a projective displacement representation for coping with this special kinematics. Next, we present the proposed new parallel manipulator structure and study its geometry and motion decouplebility. Accordingly, we solve the inverse kinematics problem by taking the advantage of motion decouplebility. Then, via the screw system approach, we carry out the Jacobian analysis for the manipulator, by which the singular configurations are identified. Finally, we analyze the reachable and collision-free workspaces of the proposed manipulator and conclude the feasibility of this manipulator for the application in minimally invasive surgery.

This paper presents a design concept for gravity compensation of planar articulated robotic arms using a series of gear-slider mechanisms with springs. The spring-attached gear-slider mechanism has one degree-of-freedom (DOF) of motion, which can serve as a gear-spring module (GSM) to be installed onto the robot joints for leveraging the gravitational energy of the robot arm. The proposing GSM-based design is featured by its structure compactness, less assemblage effort, ease of modularization, and high performance for gravity compensation of articulated robotic manipulators. As a key part of the design, the stiffness of the spring in the GSM can be determined through either a design optimization or an analytical approximation to perfect balancing. The analyses on several 1-, 2-, and 3-DOF GSM-based robot arms illustrate that the analytical approximation to perfect balancing can reach nearly the same performance as provided through the design optimization. The power loss due to the gear contact is considered when evaluating the gravity compensation performance. A formula for spring stiffness correction is suggested for taking the power loss into account. An experimental study on a one-DOF GSM-based robot arm was performed, which shows that a power reduction rate of 86.5% is attained by the actuation motor when the GSM is installed on the robot arm.

The mechanisms with variable topologies (MVTs) are usually changing their topological structures in accordance with the varying mobility and quasi-singular configurations. The mobility analysis and configuration singularity of MVTs are studied via screw theory in this paper. The configurations of MVTs are formulated by a set of variable combinations of screw coordinates. For the mobility analysis, two examples provided show that the proposed approach is adoptable for dealing with common MVTs. For the configuration singularity, the concepts of stationary configuration and uncertainty configuration are utilized to demonstrate the topology varying strategy of MVTs. The result in this work provides the theoretical basis and inspiration for the configuration synthesis and analysis of mechanisms with variable topologies.