This paper deals with a 2-DOF (degrees-of-freedom) 3-4R parallel manipulator (PM) with planar base and platform—a novel PM with multiple operation modes (or disassembly free reconfigurable PM) that can use the minimum number of actuated joints. At first, a set of constraint equations of the 3-4R PM are derived with the orientation of the moving platform represented using a Euler parameter quaternion (also Euler–Rodrigues quaternion) and then solved using the algebraic geometry method. It is found that this 3-4R PM has six 2-DOF operation modes, including the two expected spherical translation mode and sphere-on-sphere rolling mode when the PM was synthesized. The motion characteristics of the moving platform are obtained using the kinematic interpretation of Euler parameter quaternions with certain number of constant zero components, which was presented in a recent paper by the first author of this paper, instead of the eigenspace-based approach in the literature. The transition configurations, which are constraint singular configurations, among different operation modes are also presented. This work provides a solid foundation to the development and control of the 2-DOF 3-4R PM with both 2-DOF spherical translation mode and 2-DOF sphere-on-sphere rolling mode.

This paper deals with a 6R single-loop overconstrained spatial mechanism that has two pairs of revolute joints with intersecting axes and one pair of revolute joints with parallel axes. The 6R mechanism is first constructed from an isosceles triangle and a pair of identical circles. The kinematic analysis of the 6R mechanism is then dealt with using a dual quaternion approach. The analysis shows that the 6R mechanism usually has two solutions to the kinematic analysis for a given input and may have two circuits (closure modes or branches) with one or two pairs of full-turn revolute joints. In two configurations in each circuit of the 6R mechanism, the axes of four revolute joints are coplanar, and the axes of the other two revolute joints are perpendicular to the plane defined by the above four revolute joints. Considering that from one configuration of the 6R mechanism, one can obtain another configuration of the mechanism by simply renumbering the joints, the concept of two-faced mechanism is introduced. The formulas for the analysis of plane symmetric spatial triangle are also presented in this paper. These formulas will be useful for the design and analysis of multiloop overconstrained mechanisms involving plane symmetric spatial RRR triads.

The parallel metamorphic mechanism is a novel metamorphic mechanism. Its kinematics analysis is not only a new research field, but also a difficult problem. In this paper, with the origin of coordinates on the moving platform describing its position and Euler angles describing its orientation, we present the quaternion expression of an arbitrary point’s location on the moving platform in the fixed coordinate system. Then a method to establish the unified mathematical model for kinematics analysis of the parallel metamorphic mechanism is presented. Based on this unified mathematical model, forward and inverse kinematics analysis of the parallel metamorphic mechanism in different configurations can be conducted. Using kinematics analysis of a novel 4-URU parallel metamorphic mechanism, the proposed kinematics analysis method is further elaborated, and the resultant elimination method is presented to solve the kinematics equations. Finally, a numerical example is given to verify that the proposed method is correct and effective.

This paper presents an approach to the configuration synthesis of metamorphic mechanisms with consideration of both link and joint changes. The technique, referred to here as computational geometry, uses a constraint graph to represent topological structure of metamorphic mechanisms instead of traditional graph representation that can not distinguish link types and multi-joints. Based on the constraint graph, a characteristic incidence matrix is proposed with the characteristic relationships between links and joints. Then, a synthetic method based on characteristic incidence matrix is put forward in this paper using operations among matrixes with different orders by binary computing. Through an example of a four-bar mechanism synthesizing into five-bar mechanisms with the proposed configuration synthetic method, it is confirmed that the approach is correct and effective for the configuration synthesis of all metamorphic mechanisms with single or multiple joints.