3. Kinematic Analysis Klann Linkage

The Motion of the Crank the Coupler:

I decided to model the movement of the crank and the coupler links along with the angular displacement. The crank would be powered by the rotational motion of a gear that is meshing with another gear connected to a handle/windmill. Ideally, this mechanism would be able to be powered by the wind and provide the walking motion.

Here’s the code and plot of the crank movement:

Figure 6: Code for the Position Analysis of the Crank

Figure 7: Position of the Crank

Figure 8: Code for the Position and Total Angular Displacement

Figure 9: Angular Displacement for Theta 3 and Theta 4 of the 4-bar

Figure 10: Position of the Coupler

To make sure these position results made sense, I decided to go to SolidWorks and take snapshots of the mechanism with the crank angle varying 45 degrees each step. I was able to get the following results:

0 Degrees:   45 Degrees:  

90 Degrees:135 Degrees: 

180 Degrees: 225 Degrees: 

270 Degrees: 315 Degrees: 

Figure 11: Position of Links at 45 Degree Intervals of the Crank

Combining these results produced the following motion, which goes hand in hand with my MATLAB results (red). I tried different methods, but I could not figure out a way to show the motion of the other moving positions (orange). This would be something that would require using the motion of the 4-bar mechanism as input and take into account the big link that makes up the leg with two joints, and the rocker that allows it to move back and forth from the top.

Figure 12: Position of the Joints and Foot as the Crank Angle Changes

Using the following gears from the Karakuri book I plan to transmit the rotating motion of the handle/windmill (green part in the SolidWorks assembly) to the crank of the 4-bar, which would eventually transmit this motion and produce the motion shown above and allow the leg to walk.

Figure 13: Gears from the Karakuri book

The gear ratio “R” of this subsystem would be the following, where Nin is the number of teeth in the driver gear (6) and Nout is the number of teeth in the driven gear (12):

Therefore, from the input velocity by the wind/user, the output velocity would be half of this magnitude.

This video shows the desired movement of the leg.