Here is what I understand about using Minimum Constraint Design:
1) Support and guide each body only at points, and as few points as possible, to get the desired performance.
Example: Building only 3 legs for a chair, since 4 is redundant. The disadvantages of this are that the chair may be less stable and that less points of stress means more stress on those points.
Virtually all examples of minimal constraint design seem to involve tripods or otherwise 3-legged things.
2) Provide only the minimum number of constraints needed to permit the degrees of freedom desired and no others, allowing no looseness.
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Legos are good examples of MinCD because they allow little or no room for looseness in both moving and nonmoving parts moving parts are held in place using only a minimum number of constraint points.