# Design and Accuracy Analysis of a Micromachine Tool with a Co-Planar Driving Mechanism
## 1 Introduction
The main features of the proposed machine include: (1) tilt-drive mechanism. This has a high precision resolution with a fixed full stroke, and can reduce the size of the machine and the number of key parts, thus reducing the sources of potential error, as well. (2) Co-planar multi-DOF platform. The mechanism uses three sets of drive mechanisms with slide rails and bearings, which allows the platform to have an X-, Z-axis translation movement and a B-axis rotation. In addition, the machine weight can be greatly reduced, and the cumulative error between the servo shaft load and the platform can be also reduced. Because micromachine tools have very strict requirements with respect to the static/dynamic rigidity of the structure itself, the optimal structure/configuration design were confirmed on the basis of static/dynamic stiffness and dynamic compliance analysis, kinematic analysis, hybrid error analysis in this study to ensure that the expected high accuracy of the machine was achieved. In addition, the influences of major error sources in key components on the accuracy of the proposed machine were determined in order to provide guidelines for the detailed machine design. Furthermore, kinematic equations were derived to analyze the following motion characteristics: (a) the relationship between platform feed resolution and tilt-drive angle, (b) the relationship between X and Z travel of the co-planar platform and tilt-drive angle, (c) the relationship between platform rotation resolution and rotation angle, (d) the displacement, velocity and acceleration of platform translation and rotation characteristics, (e) the relationship between spindle seat feed resolution and tilt-drive angle, (f) the relationship between Y-axis travel and tilt-drive angle, (g) the analysis of the displacement, velocity and acceleration characteristics of the spindle seat. When designing the tilt-drive angle and working travel range for the co-planar multi-DOF horizontal machine tool, the kinematic characteristics analysis can be used to confirm whether the design of the tilt-drive angle and related dimensions is able to meet the requirements of the machine design specifications. In this study, the D-H rule and the homogeneous coordinate transformation matrix in robotics theory were used to establish the kinematic model. Error sources were added to the kinematic model in order to establish the total error model of the machine. This error model can be used for sensitivity analysis to determine the sensitivity parameters of the major error sources, and thus to evaluate the influences of the error sources on the accuracy of the machine. Due to the advantages of co-plane synchronous driving mechanisms, the micromachine does not need to use a high-end servo drive system and CNC controller to achieve high feed resolution and high accuracy. Because the major driving units lie on the same plane, the machine has a low center of gravity and low movement inertia, resulting in stable and accurate movement. Finally, a prototype of the designed machine was built, and machining experiments were carried out to verify the feasibility and effectiveness of the design. The experimental results showed that the design was feasible and effective. The structure of this manuscript is as follows. In Section 2, the principle of the co-plane platform is elucidated. In addition, the kinematic characteristics of the machine tool structure are analyzed. In Section 3, the error model of the proposed machine is developed and used to explore the relationship of between the major error sources. In addition, sensitivity analysis was also conducted to analyze the influences of the major error sources on the accuracy of the proposed machine. In Section 4, verification experiments are carried out on the prototype machine and the results are discussed to confirm the accuracy and machinability of the proposed design and machine. Finally, the conclusions of this study are presented in Section 5.