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:

  1. 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.

  2. 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.

  3. 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:

  1. positioned relative to each other and if needed

  2. fixated relative to each other or

  3. they need to move in 1 or more directions relative to each other.

The generic cases of suppression of degrees of freedom of a cube are shown in the attachment: GenericCasesExactConstrained.pdf.

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

The suppressed degrees of freedom in the above attachment

0T

1T

2T

3T

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, Rz

3R

Tx, Ty, Rx, Ry, Rz

Tx, Ty, Tz, Rx, Ry, Rz

See the section: Exact Constrained Examples for examples.


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