-- JonathanKarpick - 01 Jun 2004
minor additions 01 Jun MarkCutkosky

Go to bottom of this page for the zipped archive of matlab files. See TrajectoryAnalysis for general explanation of coordinates and a powerpoint presentation.

TrajectoryAnalysis, as deciphered by Jonathan K.:

File description:
trajectory.m - Matlab File that runs the trajectory analysis
riseconfig.m - specifies the geometry of the leg, and saves it to the riseconfig.mat
fourier_fit.m - fits curves to desired vs. and vs. trajectories


  1. Runs riseconfig.m
    • sets physical constants for linkage (see diagram)
    • sets constants for radii of the gears in the differential
    • sets number of time steps used for a full period of the leg trajectory
    • set the time for one cycle of the foot
    • specify vs. and vs. by using two arrays evenly spaced in time - they will be normalized so that a cycle is completed in the time given (from above)
  2. Runs fourier_fit.m
    • generates fourier coefficients for vs.
    • generates fourier coefficients for vs.
  3. Computes x and y positions of the foot, in the four-bar plane, for one revolution of , in num_steps
  4. Generates a table of (crank angle) to (trajectory angle) for later reverse table look-up (does equal steps between 0 and 360 degrees based on num_steps in riseconfig.m
    • Estimates as the distance around the arc by using straight line distances between the points.
    • is then normalized and scaled (by n??)
  5. Generates equations for and based on the fourier fits.
  6. Generates a , matrix based on the above equations, for equal steps in
  7. Generates a , matrix based on the above equations, for equal steps in
  8. Plots vs. and vs.
  9. Calculates a time vector using desired vs and then scales it to match desired period. Maybe a little more info on this? - jk, 02jun04
  10. vs time is determined by linearly interpolating the vs. table now that vs. time is known
  11. Ditto with vs. time
  12. Calcluates vs. time and vs time (the motor angles given the differential)
  13. (Still working on how to label 3-D trajectory with the values of )
  14. Plots the 3-D trajectory

Matlab files contained in attached Zip file:

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