# Kinematic Analysis and Verification of a New 5-DOF Parallel Mechanism
## 5 Experiment  
The whole prototype is made of profiles with side length of 20 mm, and the lead screw module and profiles are connected by connecting plates. The whole 5-DOF parallel mechanism is composed of moving platform, upper and lower plates, ball screws, driving limbs, restraining limb, connecting plates, Hook joints, and spherical hinges. The lower plate in this paper is also called fixed platform. The 3D model and physical model are shown in Figure 19.  
The diameter of the link is 8 mm, the length of the link is 205 mm; Diameter, lead, and effective stroke of ball screw are 16 mm, 5 mm, and 205 mm respectively; the base size of the moving platform is a square with a side length equal to 80 mm, and the coordinates of the center positions of the five spherical hinges are \((35,\ 51)\), \((-35,\ 51)\), \((-51,\ -35)\), \((51,\ -35)\), \((0,\ 51)\); the slider is connected to the Hook joint on the driving limb through the inclined plate, and the angle between the two planes of the inclined plate is \(120^{\circ}\). In addition, the center points of five Hook joints connected with the slider are evenly distributed on a circle with a radius of 135 mm.  
In order to check the degree of freedom of the mechanism and measure the motion accuracy of the moving platform actuator, the posture angles of the moving platform are now set to \(\alpha=0^{\circ},\ \beta=0^{\circ}\) and \(\alpha=0^{\circ},\ \beta=-5^{\circ}\). We fixed a pencil on the moving platform, and the axis of the pencil is required to be perpendicular to the plane of the drawing paper and a circle with a radius of 30 mm is drawn to verify the space motion function of the device. The track of the circle is planned and the reference speed of the moving platform is 10 mm/s.  
During the experiment, the tip of the pen starts from the coordinate origin \(o\). Firstly, the moving platform moves 5 mm in the positive direction of \(Z\)-axis, then moves to the right first above point \(A\). The moving platform moves 5 mm in the negative direction of \(Z\) axis and the pen tip falls at point \(A\). Then, go through \(B,C,D\) counterclockwise and back to point \(A\). Finally, the moving platform moves up, the pen tip leaves the paper, and the experiment is completed. Among them, when drawing a circle with the posture angle \(\alpha=0^{\circ}\) and \(\beta=-5^{\circ}\) and the moving platform moves from directly above the origin to directly above point \(A\), not only does the distance change but also \(\beta\) changes from \(0^{\circ}\) to  
Figure 19: Prototype of parallel mechanism.  
\(-5^{\circ}\) during this process. From this, the rotational freedom of the parallel mechanism can be verified.  
The experimental results of drawing a circle in two situations with posture angles \(\alpha=0^{\circ},\ \beta=0^{\circ}\) and \(\alpha=0^{\circ},\ \beta=-5^{\circ}\) are shown in Figure 20.  
The coincidence point A of the circular trajectory can indicate that the trajectory of the parallel mechanism has good coincidence, and the successful drawing of circles in two cases of \(\alpha=0^{\circ},\ \beta=0^{\circ}\) and \(\alpha=0^{\circ},\ \beta=-5^{\circ}\) illustrates the mechanism meets the design requirements of three-dimensional movement and two-dimensional rotation freedom. Due to the gap of hook joint and spherical hinge and the error of connecting link length, the motion error of moving platform is large. When the posture angle is \(\alpha=0^{\circ}\) and \(\beta=0^{\circ}\), the roundness error of the circle is 2 mm, and when the posture angle is \(\alpha=0^{\circ}\) and \(\beta=-5^{\circ}\), the roundness error of the circle is 1.5 mm. How to further improve the motion accuracy of the moving platform is worthy of further study in the next step.