All previous research on design of parallel robots relates to analyzing and optimizing the kinematic geometry without regard to the equilibrium configurations of the parallel robot with flexural pivots once the external load is assigned. This article addresses the equilibrium configurations of a planar 3-dof parallel robot with flexural pivots. A system of four coupled transcendental equations with trigonometric functions in four unknowns is derived from the inverse static analysis. The initial configurations of the parallel robot are discussed firstly, then a numerical method is presented based on the Newton’s iterative method, which can find all the real roots of the system of transcendental equations with trigonometric functions without initial value selection in the specified intervals to detect the entire set of the initial configurations and the equilibrium configurations of the parallel robot with flexure hinges. Finally, a numerical example is provided.

We present the approaches to motion planning for a spherical robot with a stable platform, which is not a nilpotent system. Firstly, the kinematic equations of the spherical robot are changed into an affine nonlinear control system without drift. The procedure starts by computing a control that steers the given initial configuration to the desired target configuration for an extended system using a Philip Hall basis of the controllability Lie algebra. The motion planning algorithm for the extended system is proposed. The solution to motion planning for the original system is then obtained using the Philip Hall coordinates. An iterative algorithm is given to generate arbitrary precision, and two methods of motion planning for the spherical robot are summarized. Finally, the simulation results of the motion planning examples illustrate the effectiveness of the methods.

Function is the most crucial concept in designing better and more innovative products. Function modelling is a critical step in the product design process. A modelling technique using the Petri Nets (PN) for function representation is presented based on the black box method and the theory of function basis. The characteristics of function modelling are summarized firstly. Then the feasibility of function modelling based on PN is demonstrated. The PN model provides easy graphical representation for visualization of function analysis. Finally the example of attaching a cap to a tube of toothpaste using automated equipment is given to illustrate the modelling technique of conceptual design. The functional model established in this work can completely describe the dependencies between flows and functions, and will make computer tools available that support functional design and innovative design in the future.

Geared linkages are useful mechanisms, which can be formed by combining planar linkages with one or more pairs of gears. As a result output motions can be obtained with reversing, nonreversing without dwell or nonreversing with dwell. As an example consider the design of the regressive or irregressive two-gear four-bar linkages with prescribed dwell characteristics. First of all, a simplified algorithm is given, including relevant analytical solutions and the crank existing conditions. Then the homotopy iteration method is introduced to solve the non-linear equations, all solutions can be found easily without choosing proper initial values. Finally the numerical examples illustrate the synthesis procedures.

Proceeded from the topological characteristics of Geared Linkage Mechanisms(GLM) structure, a fully new graph, combinatorial graph, which can be used to describe the topological relationship in a Geared Linkage Kinematic Chain(GLKC), is firstly proposed. Then the corresponding matrix, combinatorial matrix, and the structural invariants of GLKC are presented. Based on the structural invariants, this paper establishes a systematic procedure for detecting isomorphism among GLKCs using the powers of combinatorial matrix. A computer program based on the procedure has been applied successfully for detecting isomorphism among both the planar kinematic chains as well as GLKCs.