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.

从同构的图论意义出发，提出了一个新的运动链结构不变量，进而提出了利用邻接矩阵的幂序列进行运动链同构判定的方法。它与现有的其他方法相比，具有直观、简便和显明图论依据的特点， 且该方法不仅可以实现运动链的同构判定，而且可以成功地判定一般图的同构。在此基础上，本文最后给出了从同一运动链中识别出不同机构的两个方法。

研究了一种全向滚动球形机器人的动力学建模、分析与仿真方法. 根据机器人所受的非完整约束，建立了其运动学模型. 根据机器人的结构特征和Lagrange-Routh方程，建立了其动力学模型，给出了消去未知Lagrange乘子的策略. 得到了该球形机器人的完整动力学模型，即控制机器人运动的强耦合二阶微分方程组. 建立了描述该球形机器人完整动力学方程的仿真模型. 运动实例的动力学分析和仿真结果验证了该方法的有效性.

设计了一种全向滚动球形机器人的内驱动机构，4台直线电机分别在4个空间对称的轮辐上径向移动,改变系统重心位置，驱动球形机器人在平面上全向滚动. 基于球体纯滚动的非完整约束和步进直线电机运动的离散特性，建立了球形机器人的运动模型，给出了控制其运动的二阶微分方程组，进而提出了该球形机器人的轨迹规划算法. 结合实例进行了运动分析和轨迹规划仿真，表明这种运动分析模型是正确的，并且简化了球形机器人的驱动装置,降低了能耗.

使用UG NX和ADAMS，研究了一种具有稳定平台的、非完整的全向滚动球形机器人的虚拟样机建模和运动仿真。通过对球形机器人虚拟样机模型的转化，解决了ADAMS软件不支持球壳与平面间的约束，无法模拟球壳在平面上滚动的问题。结合典型实例，对球形机器人的运动情况进行了仿真。仿真结果表明该球形机器人的内置稳定平台在球体全向滚动过程中始终保持稳定的姿态，而不随球体一起滚动。这为物理样机的研制提供了可靠的参考依据。

提出了一种具有稳定平台的全向滚动球形机器人装置. 该球形机器人由装在球体内部、相互垂直布置的两台伺服电机驱动，可在平面上全向滚动. 在球形机器人内部有一个稳定的仪器、设备搭载平台，这个平台在球体全向滚动过程中始终保持稳定的姿态而不随球体一起滚动. 介绍了该球形机器人的结构原理，基于其运动的非完整约束，利用广义欧拉角给出了其运动微分方程，建立了该球形机器人的运动学模型，结合实例对该球形机器人进行了运动分析和仿真.