# Design and Accuracy Analysis of a Micromachine Tool with a Co-Planar Driving Mechanism
## 2 Principle of the Co-Plane Platform  
### Principle  
The horizontal-type co-plane multi-DOF micromachine tool was designed using a simple co-plane synchronously driven platform (Figure 1), which provides translational motion along the X- and Z-axes, rotation around the B-axis for the work table, and Y-axis translation (up and down movement) for the machine spindle. Compared with conventional serially stacked CNC machine tools, as a result of the co-plane platform not having a serially stacked structure, it does not require a large amount of driving power for the feed system on the lower level to move large structural masses, and it also will not encounter large amounts of movement inertia while it is moving. The platform uses three sets of tilt-drive mechanisms with rotating bearings arranged in a circular array. By controlling the drive shafts, the platform can have linear movement along the X-/Z-axes, as well as B-axis rotation. The driving unit of the platform consists of a ballscrew and a sliding rod, placed in a triangular geometry, thus achieving precise and high feed resolution due to the triangular proportional transformation. Furthermore, a double-column structure was designed for the machine spindle in order to provide Y-axis machining movement. Figure 1: Scheme of co-plane platform, (**a**) X-, Z- and B-axis motion, (**b**) the micromachine tool. As shown in Figure 1, the co-plane platform consists of three sets of tilt-drive ballscrew servo system (A, B, and C in Figure 1) with the same tilt angle. The ballscrews with sliding rods (D, E, and F in Figure 1) are used to drive the platform to move in the X and Z directions. The ballscrew, sliding rod, and platform are connected by three movable linkages (L1, L2, L3). The sliding blocks on the sliding rods are respectively fixed at the three points (P1, P2, P3) with the work table. The three connection points are equidistant from the center of the work table, and are located on the center of the work table as the center of circle. When the feeds of sliding blocks are appropriately controlled, the table can conduct rotation about Y-axis. When this mechanism is applied to a micromachine tool, the machine can perform linear movements along the X- and Z-axes, as well as B-axis rotation (Figure 1). As shown in Figure 1, when the A and C ballscrews are fixed and the B ballscrew is moving, the linkage L2 pushes the table to move along the X direction. The linkages L1 and L3 and the sliding rod E provide the function of movement guidance. When the B ballscrew is fixed, the A and C ballscrews move in the same direction at the same speed, while linkages L1 and L3 move the table along the Z-axis, as shown in Figure 1. At this time, sliding rods D and F and linkage L2 provide the function of movement guidance. When ballscrews A, B, and C are moving in the same direction at the same speed (CW or CCW), the moving paths of the three connecting points (P1, P2, P3) are the distances from each connecting point to the center of the platform (as shown in Figure 1), which drives the platform for rotational movement about the center of the platform. The bearing on the sliding rod provides rotational DOF to rotate the platform around the center of the platform. This design provides 3 DOF movements (linear, moving along the X- and Z-axes, and rotation about the Y-axis) with a lighter inertia effect, and can also reduce the loading of the servo control system. Because the ballscrew drives operate using a tilt servo mechanism principle, the triangle geometric motion transformation will proportionally reduce the movement of the work table so that finer feed resolution can be achieved for the work table, and the errors caused by ballscrew backlash and pitch error can also be reduced. Because of the advantages mentioned above, the machine is able to achieve the high resolution and high precision required for micromachining without the use of high-end driving components or a CNC controller. Figure 2a shows the ballscrew using the tilt-servo mechanism principle.