Various types of micro-motion devices have been developed in the past decade for applications including the manipulation of cells in micro-surgery and the assembly of micro-chips in micro-assembly industries. Most of the micro-motion devices are designed using the compliant mechanism concept, where the devices gain their motions through deflections. In addition, closed-loop parallel structures are normally adopted due to better stiffness and accuracy compared to the serial structures. However, the forward kinematics of parallel structures are complex and non-linear; to solve these equations, a numerical iteration technique has to be employed. This iteration process will increase computational time, which is highly undesirable. This paper presents a method of deriving a simple, linear and yet effective kinematic model based on the loop closure theory and the concept of the pseudo-rigid-body model. This method is illustrated with a 3 DOF (degree-of-freedom) micro-motion device. The results of this linear method are compared with a full kinematic model for the same micro-motion system. It is proved that the derived kinematic model in this paper is accurate and the methodology proposed is effective. The static model of the micro-motion device will also be presented. The uncoupling property of the micro-motion systems, based on the static model, will be briefly discussed.
In this paper we consider the dynamic modelling of compliant micropositioning mechanisms using flexure hinges. A simple modelling method is presented that is particularly useful for modelling parallel micropositioning mechanisms. This method is based upon linearisation of the geometric constraint equations of the compliant mechanism. This results in a linear kinematic model, a constant Jacobian and linear dynamic model. To demonstrate the computational simplicity of this methodology it is applied to a four-bar linkage using flexure hinges. Comparisons are made between the simple dynamic model and a complete non-linear model derived using the Lagrangian method. The investigation reveals that this new model is accurate yet computationally efficient and simple to use. The method is then further applied to a parallel 3-degree of freedom (dof) mechanism. It is shown that the method can be simply applied to this more complex parallel mechanism. A dynamic model of this mechanism is desired for use in optimal design and for controller design.