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The generic cases of suppression of degrees of freedom of a cube are shown in the attachment: [[attachment:GenericCasesExactConstrained.pdf]]. ||||||||||<tablewidth="506px" tableheight="188px"style="text-align:center">'''The suppressed degrees of freedom in the attachment:''' || || ||0T ||1T ||2T ||3 || ||0R ||- ||Tx ||Tx, Ty ||Tx, Ty, Tz || ||1R ||- ||Tx, Ry ||Tx, Ty, Ry ||Tx, Ty, Tz, Ry || ||2R ||- ||Tx, Ry, Rz ||Tx, Ty, Ry, Rz ||Tx, Ty, Tz ,Ry, R || ||3R ||- ||- ||Tx, Ty, Rx, Ry, Rz ||Tx, Ty, Tz, Rx, Ry, Rz || |
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Exact constraint design
Exact constraint design, see also [Skakoon2008], is one of the most important lessons I had to learn in my career as a Mechanical Engineer. I had to learn it the hard way by making many mistakes. In short:
Never limit more degrees of freedom than absolutely needed, when mating parts, with an absolute maximum of 6 namely 3 translational and 3 rotational degrees of freedom.
For each free degree of freedom of movement (R=Rotation, T=Translation) needed between two parts one less degree of freedom needs to be constrained. The sum of constrained and free degrees of freedom of movement is always 6, namely 3 translational and 3 rotational degrees of freedom of movement.
Use force-closure to mate parts, never use form-closure, thus never use matching contra-forms to mate parts.
Mechanical products very often consist of many parts which need to be assembled or need to move/rotate relative to each other. Therefore, these parts need to be:
positioned relative to each other and if needed
fixated relative to each other or
they need to move in 1 or more directions relative to each other.
The suppressed degrees of freedom in the above attachment |
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0T |
1T |
2T |
3T |
0R |
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Tx |
Tx, Ty |
Tx, Ty, Tz |
1R |
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Tx, Ry |
Tx, Ty, Ry |
Tx, Ty, Tz, Ry |
2R |
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Tx, Ry, Rz |
Tx, Ty, Ry, Rz |
Tx, Ty, Tz ,Ry, Rz |
3R |
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Tx, Ty, Rx, Ry, Rz |
Tx, Ty, Tz, Rx, Ry, Rz |
See the section: Exact Constrained Examples for examples.