Optimising What Exactly?

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It is not easy to optimise most problems have:

• multiple local optima
• multiple objectives
• objective functions may result in degenerative (useless) solutions
• constraint functions may result in degenerative (useless) solutions
• the need to start with a feasible solution

The process involves mapping out the feasibility areas and then focusing in on the most important objectives that result in the best solution.

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Finding an initial feasible solution

Fortunately we can start with DIY Walkers solution (but at half scale):

• Axle: (0.0 mm,0.0 mm)
• Hip:  (-48.0 mm,33.0 mm)
• Crank L1: 30.0 mm
• Thigh L2: 60.0 mm
• Idle    L3: 40.0 mm
• Shin   L4: 70.0 mm
• Knee Angle: 90.0 degrees

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Here the foot trace down range is 120 degrees between the green markers and 180 degrees inclusing the green markers:  

Note how the foot trace slow down near each left/right extremes, and is very fast when the foot up.

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Extending the Flat Bottom Range

The first major objective identified was the need to have a flat bottom (as much as practical):

While this objective has been meet for 120 degree range (suitable for a three leg walker). How ever foot lift has been lost.

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A Symmetry Constraint

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For symmetry, the difference between each Y point at each horizontal extreme is minimise, using:

• DeltaY = ABS(Yfwd-Ybwd)
• Minimum mid-section upper and lower range of 10.0 mm

Here is the result:

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Using this as an initial feasible solution, we can impose a flat bottom:  

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The final walker parameter are:

• Axle: (0.0 mm,0.0 mm)
• Hip:  (-53.1 mm,52.5 mm)
• Crank L1: 30.0 mm
• Thigh L2: 60.0 mm
• Idle    L3: 59.3 mm
• Shin   L4: 60.0 mm
• Knee Angle: 90.0 degrees

Reducing the minimum mid-section upper and lower range to 5 mm for the final result:

Note the flat bottom has been optimised for 120 degrees
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The same design as imported into a CAD package:

Note the cyan bottom range is for 180 degrees.

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This is what I see after my optimiser runs:

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Clearly the 4 bar linkage can be used for a three foot (120 degree) walker, but its use would be best for relatively smooth floors as the minimum clearance is about 5.0 mm (for a 94 mm step).

The cyan vertical range (for 180 degrees) is about 3.5 mm, suggesting a two foot (rather than three foot) walker is possible, but perhaps some what bumpy ride.

AlanX