Kinematic Analysis of MMTDA

Each of the bars is calculated based on the mechanical properties of the frame of the quadcopter we use. For the calculations, we simplified the prerequisite values considering the limitation of the chassis shown below.

Figure 1. Prerequisite Value Calculations

1. The coordinate system is centered at the midpoint of the two moving gears.
2. The end point of the fixed bar is set based on its length of 200mm and position in θ = 45° & φ = 10° in the spherical coordinate system.
3. The radius coordinate of the gears’ (In the code ‘disks’) which is mounted on the gear located on the bottom of the body frame with two moving bars.
4. For the motor plates the distance between the three nodes(otherwise the end point of the moving gears’ location in the plate body coordinate) for connecting each of the three bars.

Figure 2. Initial Values of the Variables

Since all four propeller motors have the same configuration and are driven by the main motor, their configurations can be easily controlled by analyzing just one motor from the arm in this code.

Figure 3. Plots of Calculations

(The original code that generated this result graph has been attached to the Appendix.)

The optimized result indicates that the two bars (l_1, l_2) should be 234mm in length, respectively. Additionally, the distance between the end points of the two moving bars should be 59.76mm.

With these design specifications, the motion of the final model is as follows.

Figure 4. Animated GIF of Propeller Arm Motion