We know that each unconstrained body in space has six degrees of freedom (DOF): three translations and three rotations about X, Y and Z axes. Each mate removes a certain number of DOFs from the system. The table below shows some of the mates in SOLIDWORKS and how many DOFs that they restrict.
|Mate Type||Translation DOF Removed||Rotational DOF Removed||Total DOF Removed|
|Screw Mate||2||2 (+1)||5|
|Point to point||3||0||3|
What Are Redundancies?
Redundancies are when multiple mates remove the same DOF on a part. For example, if we create a pin joint we most likely use a concentric mate between the cylindrical faces of the pin and the hole and a coincident mate between the flat faces of these two components.
In this case the concentric mate removes four out of six DOFs including the translation along X and Y axes as well as the rotation about these axes. The coincident mate between the two flat surfaces will restrict the translation along Y axis and the rotation about X and Z axes. These two mates remove seven DOFs out of the max possible of six. This is because both of these mates remove rotation about X and Z axes.
What Happens When We Have Redundancies?
Any such duplication of DOFs can lead to over constraining your system or introduce what are known as redundant constraint equations. When you have a redundant constraint, you have two or more mates effectively fighting to control one specific DOF. In simple cases, SOLIDWORKS will automatically remove a redundant constraint equation to stop the redundancy. But in complex situations it may not remove the correct one for the mechanism that leads to the wrong motion or answer.
To verify that we can run a motion study and add a gravity to it. When we run the study, it will show the number of redundancies next to the Mates folder. If you right clicking on the Mates folder and selecting Degrees of Freedom, it shows a list of DOFs and the redundancies in the mates.
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