# Leg mechanism
## 5-bar mechanisms as 2-Dof legs
### Prior art & My Design
In the article [1], the authors designed some parts (a, b and d) to strengthen the original leg-mechanism of the Minitaur. They also redesigned the joints ( c ) for smoother rotation by adding two thrust ball bearings .
In my design, I made the joints more compact in its axial direction by replacing the two thrust ball bearings with one deep groove ball bearing. The compact joints not only use fewer bearings but also have better mechanical properties; since the bars of the 5-bar leg-mechanism set closer to each other in the axial direction of the joints, the shoulder bolts in the center of the joints might bear less bending moment. Such bending moment could cause additional friction between the bars and the bolts. With less bending moment on the bolts, the leg-mechanism might have better force transmission.

The only problem of my leg-mechanism design is insufficient axial strength of the deep groove ball bearings. I use NSK 604ZZ bearings in my design; acordding to SKF General catalogue, the 604ZZ bearings could hold 70N axial load. Since my robot is about 5~6 kg, the 604ZZ bearings in my leg-mechanism are far strong enough to hold the weight.
### Static Structure Simulation
Before sending the engineering drawings of the leg-mechanism to machine workshop, I should roughly evaluate the toughness of the mechanism.

Firstly, I have edited an [EXCEL file](https://drive.google.com/open?id=1KH0fRZlkv3DFrMpVrr0Xd2jMPvRJsdREkdkqCUO_gQc) to analyze the leg-mechanism. Calculating the transmitted force of the leg-mechanism through the EXCEL file, I set some limitations on it: 3 N-m maximum motor torque, 10 cm length of the two short bars, 20 cm length of the two long bars, and 40 to 300 degrees for the angle between the two short bars. Within those limitations, the maximum transmitted force on the bars is 112 N.

Secondly, although the leg-mechanism is 2-DoF, it still needs to take lateral force into account. I expect each leg-mechanism could hold 70 N (greater than the weight of my robot) lateral force on their own.

According to the limitations mentioned above, I set the boundary conditions for the static structure simulation shown below.
Boundary Conditions for the simulation of the short bar
Boundary Conditions for the simulation of the two kinds of long bar

To precisely simulate stress concentration effect, I locally refined the mesh in the simulations.

The equivalent stress results of the simulations are shown below. The material of the bars is Aluminum Alloy 6061-T6, which has 276 MPa Yield Strength. I only need the simulation stress below 276 MPa. Even though the aluminum alloy has low fatigue strength, my leg-mechanisms would be strong enough for the short-term test of my robot.

For the short bar and the second long bar, the toughness is high enough to hold the maximum transmitted force (112 N) and the 70 N lateral force at the same time. For the first long bar, however, the lateral force (70 N) could lead to significant damage. Since the 70 N lateral force is actually a harsh load for the leg-mechanism, a 60 N lateral loading capability (equal to the weight of my robot) would be acceptable for my application.
Change the lateral force boundary condition to 60 N.
The equivalent stress result shows that the toughness of the first long bar is high enough to hold the loads.

### Parts & Assembling
Here are the parts of the 5-bar mechanisms.
Fastening the bearings into the bars with thread-locking fluid.
Completed leg-mechanisms and BLDC motors
## Reference
[1] Daniel J. Blackman, John V. Nicholson, Camilo Ordonez, Bruce D. Miller, and Jonathan E. Clark "Gait Development On A Direct Drive, Quadrupedal Robot"