About Degrees of Freedom
Understanding the meaning of degrees of freedom is critical to selecting the appropriate constraints to define a mechanism’s ability to move. The number of degrees of freedom (DOF) represents the number of independent parameters required to specify the position or motion of each body in the system.
A predefined constraint set defines a connection between two bodies. The constraints in the set act as restrictions on the motion of bodies relative to each other, reducing the system’s total possible degrees of freedom.
A completely unconstrained body has six degrees of freedom, three translational and three rotational. Each constraint restricts movement in a specific way. For instance, if you apply a pin connection (which only allows rotational movement about an axis), to a body, the degrees of freedom for that body are reduced from six to one.
Before you select a predefined constraint set to apply to your model, you should know which type of movement you want to restrict for the body and which type of movement you want to allow.
General and 6DOF Connections
Use a general connection to represent a connection that has the same DOF you want to define for a specific component. There are general connections that have the same number of DOF as other connections (for instance, a ball, cylinder, or a pin connection). After you create a general connection, it appears on the model as a coordinate system. Its DOF are shown as translational and rotational arrows.
You can use a 6DOF constraint to indicate a connection that has three rotational and three translational motion axes. The motion of the model's components relative to one another does not change because no actual constraints are applied. The 6DOF connection can be reused to apply servo motors or to model a specific type of connection.
The number of rotational degrees of freedom in a 6DOF or a gimbal lock connection may be reduced by one when the connection is in a gimbal state. In this case the total DOF would also decrease by one.
|
Total Degrees of Freedom
|
Rotation Axis
|
Translation Axis
|
Connection Type
|
Constraints associated with specific DOF
|
|
0
|
0
|
0
|
Weld—Glues two bodies together.
|
|
|
0
|
0
|
0
|
Rigid—Glues two parts together while changing the underlying body definition. Parts constrained by a rigid connection constitute a single body.
|
|
|
1
|
0
|
1
|
Slider—Translates along an axis.
|
Plane-plane coincident
|
|
1
|
1
|
0
|
Pin—Rotates about an axis.
|
|
|
2
|
2
|
0
|
General
|
Point-point align if the point is on an edge.
Edge on plane.
|
|
2
|
1
|
1
|
Cylinder—Translates along and rotates about a specific axis.
|
Point on line
Plane-plane orient
|
|
2
|
0
|
2
|
General
|
Edge on plane provided the plane is neither perpendicular nor parallel to the edge
Plane-plane orient
|
|
3
|
3
|
0
|
Ball—Rotates in any direction.
|
Point-point align
|
|
3
|
2
|
1
|
General
|
Edge on plane
Point on line (line and edge must align)
|
|
3
|
1
|
2
|
Planar—Bodies connected by a planar constraint move in a plane with respect to each other. Rotation is about an axis perpendicular to the plane.
|
Plane-plane coincident/parallel
|
|
3
|
0
|
3
|
General
|
Plane-plane orient
Plane-plane orient (not parallel to the first set of planes)
|
|
4
|
3
|
1
|
Bearing—Combines a ball connection and a slider connection.
|
Point on edge
|
|
4
|
2
|
2
|
General
|
Edge on plane
|
|
4
|
1
|
3
|
General
|
Plane-plane orient
|
|
4
|
3
|
1
|
Slot
|
Point on a non-straight trajectory
|
|
3
|
3
|
0
|
Gimbal—Aligns the centers of two CSYS (see below).
|
Point to point
|
|
5
|
3
|
2
|
General (see below).
|
Point on plane
|
|
6
|
3
|
3
|
6DOF—Rotates and translates in any direction (see below).
|
|
|
|
 In addition to the connection set constraints, you must consider the constraints imposed by the servo motors you apply to your model. Servo motors are enforced displacements, velocities, and accelerations that remove degrees of freedom. Be careful to apply only as many predefined constraint sets as you need to restrict the mechanism's movement. If you overconstrain the mechanism, you will have redundancies, which can give inaccurate reaction results in dynamic analyses.
For more detailed information on component placement and constraint sets, search the Assembly area of the Help Center.
|