Worked from home - 4pm to 8pm
1. More testing on code - drew some conclusions (2 hours)
2. Further work on program to calculate effect of solid friction (~1 hr)
3. Updating blog (45 mins)
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1
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ProblemOf the 3 mass properties to be equalized for the 2 legs currently, the inertias (about hip) and m*y have large differences (~1600 kg.cm^2 and ~20 kg.cm), compared to the differences in m*z (~ 2 kg.cm). Hence either the input distance(s) to the program must be large (to get reasonably low masses to be added ), or we should expect high masses to be returned by the program for location inputs that are all close to the hip axis.
Approach
I wanted to keep it simple -> The analysis is for the case of 3 masses to be added. We would have a simple (linear) system with 3 equations and 3 unknowns.
Importantly, we always get the new differences in the 3 mass properties to be exactly equal to zero. I) Now, to equalise 'm*z' (which is low) I only added a mass on the outer leg that is off-plane but has no y-moment. This is the only mass with a z-moment.
II) Similarly to equalize the large difference in inertias we will have a second mass far away from the hip-axis but without a z-moment.
III) I arbitrarily chose a y-location for the the third mass but again this has no z-moment (could be on either leg, we just get negative values with the same magnitude).
This simplicity in the location of masses helps in drawing conclusions, I feel. Also this may help in actually adding the masses as well.
ResultsIf the second mass is kept at distances less than 35 cm (below hip axis), we get large values for sum of masses (6.1 kg and higher). With y = 40 cm for the second mass and varying location of the third mass (10,15, 20, 25, 30) the sum of masses is 3.2 kg. Simliarly y = 45 cm, y = 50 cm, y = 55 cm were tried and this further reduces the sum to as low as 1.7kg (y = 55cm). For all the above locations, the sum was least (and more or less constant) when the third mass was kept between 20 - 25 cm.
Consequences
* large y-moment of second mass about the hip axis leading to :
a) greater influence on the motion of the outer leg when it is the stance leg.
b) helps in swing of inner leg for first half of the motion (until vertical), and opposes motion for the second half.
c) reduces opposing moment when the inner leg is stance leg, as the second mas is closer to the ground.
At any rate I feel adding the second mass below the hip-axis is better than adding it above it - this would really increase opposing torque when the inner leg is stance leg.
Possible Refinements
Further reduction in sum of masses could possibly be achieved by adding a z-distance to the second and/or third masses or a y-distance for the 1st mass.
2. Program still not running, apparently MATLAB has problems with Coloumbic friction models.