## Wednesday, September 14, 2011

### Pedaling Model II

In order to solve the mechanism's movement, the next step is to define the restriction equations of the system. I chose the COG of each moving element and the angles of the thigh, shank and foot as natural coordinates, total 11 coordinates. These equations restrict 10 of them through geometrical relations and the last equation to completely restrict the mechanism was obtained in the previous post. The next step is to solve the matricial problem of the mechanism using the Newton-Raphson method. The MATLAB program created can handle any logical value of the dimensions of the elements and even a simulation with the crankarm angularly accelerated. Here you can see the parameters used for this first simulation:
And a small video of the leg movement defined by these parameters. As my 1.6Ghz laptop can't candle the MATLAB code fast enough, the crank velocity is slower than the 90rpm defined for the simulation and the movement isn't very smooth. As you can see, the ankling movement is noticeable:

Logically, all the MATLAB code hasn't been done just for a nice animation of a 5-bars system. After solving the mechanism, I've got matrices of the position, velocity and aceleration of the natural coordinates chosen every few miliseconds. These will allow me to know the inertial forces and moments acting on the mechanism and, hopefully, the forces in the pedals for a given power outpout. Moreover, knowing the weight of every element of the mechanism, I can track its COG and determine the average position during the pedaling motion of the COG of the whole mechanism that which is interesting for future dynamical studies that I will do using the program JBike6.

More soon. Thanks for reading!