Novel use of the Monte-Carlo methods to visualize singularity configurations in serial manipulators

This paper analyses the problem of the kinematic singularity of 6 DOF serial robots by extending the use of Monte-Carlo numerical methods to visualize singularity configurations. To achieve this goal, first, forward kinematics and D-H parameters have been derived for the manipulator. Second, the derived equations are used to generate and visualize a workspace that gives a good intuition of the motion shape of the manipulator. Third, the Jacobian matrix is computed using graphical methods, aiming to locate positions that cause singularity. Finally, the data obtained are processed in order to visualize the singularity and to design a trajectory free of singularity. MATLAB robotics toolbox, Symbolic toolbox, and curve fitting toolbox are the MATLAB toolboxes used in the calculations. The results of the surface and contour plots of the determinate of the Jacobian matrix behavior lead to design a manipulator’s trajectory free of singularity and show the parameters that affect the manipulator’s singularity and its behavior in the workspace.

Triple-Cell Origami Structure for Multistable Transition Sequences

With the infinite design space and the excellent folding-induced deformability, origami has been recognized as an effective tool for developing reconfigurable structures. Particularly, the multistable origami structure, which possesses more than one stable configuration that is distinct in shape and mechanical properties, has received wide research attention. Generally, the origami structure reaches a kinematic singularity point when switching among different stable configurations. At this critical state, multiple switching sequences are possible, and the actual transition is generally hard to predict. In this paper, evolving from the conventional bistable Miura-ori unit, a triple-cell origami structure with eight potential stable configurations is proposed, which serves as a platform for investigating the transition sequences among different stable configurations. To quantify the overall elastic potential of the structure, besides the conventional elastic energy originating from the rigid folding creases, extra elastic potential induced by the mismatch among the cells are introduced, so that folding of the triple-cell structure is no longer a strict single degree-of-freedom mechanism. Instead, the three cells can deform asynchronously to avoid reaching the kinematic singularity point. Hence, under displacement loading, the transition sequence of the multistable structure is predicted by performing optimization on the elastic potential energy. It shows that sequences with multifarious characteristics are possible, including reversible and irreversible transitions, and transitions with symmetric and asymmetric energy barriers. Considering that the fundamental transition mechanisms are of great significance in understanding the quasi-static and dynamic behaviors of multistable structures, the results could be potentially employed for developing morphing structures, adaptive metamaterials, and mechanical logic gates.

Kinematic analysis and optimal design of a novel 3-PRR spherical parallel manipulator

This paper introduces a novel three degree-of-freedom spherical parallel manipulator with 3-PRR topology, where P and R denote a curved prismatic joint and a revolute joint, respectively. The first revolute joint of each PRR leg is actuated via a double Rzeppa-type driveshaft, and hence underlined. The manipulator has at most eight working modes and eight assembly modes. However, only one working mode and one assembly mode of the manipulator are acceptable during its motion which can be easily identified. Singularity and kinematic dexterity analyses reveal that the proposed 3-PRR spherical parallel manipulator has no forward kinematic singularity for a wide range of rotation of the moving platform around its central axis. An optimal design of the manipulator is also presented having a workspace with good kinematic dexterity.

Optimization of the Rotational Asymmetric Parallel Mechanism for Hip Rehabilitation With Force Transmission Factors

An asymmetric three-degree-of-freedom parallel mechanism is adopted in rehabilitation robots for assisting patients suffering from stroke or trauma in the hip. It is necessary to keep its kinematic singularity out of the workspace of human normal gait and increase the output power efficiency. Therefore, a novel method is proposed to optimize geometrical parameters of the mechanism. To describe the kinematic singularity in a better way, the improved force transmission indexes based on previous methods are proposed using the reciprocal product and mobility condition of the closed-loop mechanism. The indexes mainly represent the force transmission performance of unactuated parts of subchains and moving platform. Together with the driving force transmission indexes and geometrical constraints, the multiobjective optimization model is established. The differential evolution algorithm, which is widely applied to mechanism optimization, is used to achieve optimal results. The Jacobian matrix singularity and output power efficiency along giving trajectory before and after optimization are compared to verify the effectiveness of the method.