Vertex-Splitting on a Diamond Origami Pattern

A diamond origami pattern is a well-known origami pattern consisting of identical six-crease vertices. As each vertex can be modeled as a spherical 6R linkage with three degrees of freedom (DOF), the tessellated pattern with multiple vertices is a multi-DOF system, which makes it difficult to fully control the motion in the desired symmetric manner. Here, two splitting schemes on the diamond vertex are proposed to generate three types of unit patterns to reduce the DOF. This vertex-splitting technique is applied to the multivertex diamond origami pattern to produce several one-DOF basic assemblies, which form a number of one-DOF origami patterns. Two of the one-DOF origami patterns are discussed: one of which is a flat-foldable origami pattern mixed with four- and six-crease vertices and the other is a nonflat-foldable one mixed with four-, five-, and six-crease vertices. In the one-DOF patterns, the symmetrically kinematic property of the original diamond origami pattern is well kept. Such property would significantly facilitate engineering applications comparing to the multi-DOF origami patterns. It also paves a new road to construct one-DOF origami patterns.

A novel accuracy model for the intrinsic kinematic property of a prismatic pair

A novel accuracy model is proposed to analyze the intrinsic kinematic property of the prismatic pair. The geometric error of guide rails, the elastic constrained structure of moving joints, and fixed joints are considered synthetically. The geometric error is measured by the 5D laser interferometer system with slide blocks. The elastic moving joints are equivalent to the springs, while the fixed joints to contact layers. The equilibrium equations are then set up and the analytical solution for five degrees-of-freedom errors of the moving table is revealed. The global invariant errors, including the straightness error space and the spherical image error surface, are proposed to describe the global kinematic characteristic of the moving table. Along with the comparison between the measured and theoretical indicators, the verification experiment to prove the availability of the model is carried out. As the movement of the table can be forecast precisely and evaluated objectively, the new methodology provides a theoretical basis for machine tool manufacture.

On modelling and simulation of a manipulator under consideration of a jammed joint

In this paper, the modelling of a jamming process of a joint during the operation of a manipulator is presented. Based on the kinematic property of a jamming process, a motion law of the jammed joint is chosen. By introducing a matrix corresponding to jammed joint, the equation of motion of the system is restructured without re-deriving. Some numerical simulations are carried out to illustrate the proposed algorithm.