# Design and Control of a Open-Source, Low Cost, 3D Printed Dynamic Quadruped Robot
## 2 Hardware Design
### Leg Design  
The main design goals of our 3 degrees of freedom leg is to minimize the limb mass and inertia for highly dynamic locomotion, while leveraging standard 3D printing manufacturing process. Three modular actuators, each controlling hip roll, hip pitch and knee pitch joint respectively, are serially attached to the body without additional support structure holding the joint on the other side. To minimize the leg inertia, the hip pitch and knee pitch actuators are located coaxially right next to the hip roll actuator. To actuate the knee joint from remote actuator, various mechanisms have been used, which includes linkage [11; 17; 18], timing belt [9; 19] and roller chain [20]. Timing belt and roller chain driven knee designs have two main advantages over linkage design; additional gear reduction can be easily added by using different sized pulleys or cogs, and knee joint range of motion is not limited by the linkage. As the knee joints are under the most load for legged robots, it is a common design principle to use additional gear reduction for them if the same actuators are used for both the hip pitch and knee pitch joints. In addition, the additional knee range of motion allows the robot to change the leg configurations between the knee-forward and knee-backward positions, which is not crucial for general locomotions but can be helpful for some special situations, such as climbing high stairs or using one of the limbs for manipulation. We used a four bar parallelogram linkage for knee actuation despite those advantages, as the linkage mechanism is much simpler and can be fully 3D printed. Compared to other recent quadruped leg designs that use coupler link fully housed inside the upper leg link [21], we use a longer crank/rocker links and external coupler link to lower the peak stress applied to the plastic components under load. To cope with higher load of the knee joint without using additional gear reduction mechanism, we use stronger RMD-X8 Pro actuator with 35 Nm peak torque for the knee joint, and lighter RMD-X8 actuator with 21 Nm peak torque for hip roll and hip pitch joints. To further reduce the peak stress applied to the leg parts, we used hollow squash balls without solid cores as the foot components. After testing multiple squash ball types, we found that the pro grade squash ball, which has the lowest bounce among squash ball types, provides adequate damping and shock absorption properties for our robot. Figure 6 shows the details of our leg design. Figure 5: Internal temperature over time for X8 and X8 Pro actuators. In addition to the knee joint angle limit posed by the linkage mechanism, we installed mechanical joint stops for the hip roll and pitch joints to prevent possibly catastrophic cable damage due to the over-rotation of the joints. The resulting range of motion for each joint is \(-30\lx@math@degree\) to \(30\lx@math@degree\) for hip roll joints, \(-51\lx@math@degree\) to \(93\lx@math@degree\) for hip pitch joints,and \(-134\lx@math@degree\) to \(-7\lx@math@degree\) for knee joints, which are shown in Figure 7. With the link length of 0.22 meters for both upper and lower links, each leg can produce 210 N (1.68 bodyweights) peak and 80 N (0.64 bodyweights) continuous vertical force in the fully collapsed configuration, which are only slightly less than Mini Cheetah's values of 1.7 and 0.7 bodyweights, respectively. Finally, we ran finite element analysis (FEA) simulations of the individual leg parts, assuming that the leg is in standing posture and is applied 630 N (5 bodyweights) of downward force, which is equivalent to 20 times the static downward force the robot receives when the robot is standing still. The material properties used for the analysis is shown in Table 2. Based on the simulation result, which is visually shown in Figure 8, we found that the calculated minimum safety factor to be 1.31, which means that the leg parts can withstand approximately 6.5 bodyweights before failure, despite being made of plastic material. Figure 6: 3 DOF Leg with a parallelogram linkage.