About Singularities

The physical concept of a singularity in kinematics refers to configurations in which a mechanism's number of DOF changes instantaneously. A singularity is associated with either loss or gain of degrees of freedom.

See Also
Diagnosing Computation Incidents

The Kinematics solver detects singularities directly (bifurcation singularity) and indirectly (lock-up singularity). To display the messages related to singularities, click the Incident Diagnosis command to generate the computation report. Two types of singularity are described here.

Bifurcation Singularity
A bifurcation singularity occurs when multiple
mechanism configurations are possible for the same command value. Consider a parallelogram four-bar linkage with two pairs of equal-length members. The fourth bar does not appear in the figure, it is a construction line that links the anchor points.

The four bars are aligned along the same line:

If body 1 is driven in the positive direction from the flat configuration, two types of motions are possible and equivalent:



Based on the configuration, the kinematics solver generates a message as follows:
A bifurcation singularity area occurred.
The mechanism entered or left a bifurcation singularity area. 
At crossing this area, the solver arbitrarily selects a configuration 
among several valid configurations.
The figure below describes how the kinematics solver detects the bifurcation singularity area. The bifurcation singularity occurs at the position marked 0, which lies within a small range of values known as the singularity area.(). The message generated by the kinematics solver is displayed when the mechanism enters or leaves a singularity area.

Lock-up Singularity
In a lock-up singularity, it is impossible to reach certain positions.

Consider a slider-crank mechanism. In the following configuration, the mechanism is not locked, but is free to slide back and forth. You can increase or decrease the angle value, marked Theta in the figure. The target value for Theta is 90°.



At lock-up point = 90°, the mechanism is blocked. You can no longer increase the angle value (marked in the figure). Based on the configuration, the kinematics solver generates a message as follows:
The target value is not reached.
The kinematics solver failed to reach the target value.