This topic reviews:
•  DegreesofFreedom on Parts and Joints 
•  DegreesofFreedom of a KinematicChain and the Gruebler Equation 
•  Mobility of kinematicchains 
•  DegreesofFreedom of Open and Closed kinematicchains 
Image from SOLIDWORKS 
DOF of a Part in 'Space' Parts in space have six(6) degreesoffreedom (DOF). Why six? Take the image to the left, you can see:
In MechDesigner:

When you join two Parts together, you can only move the two Parts relative to each other as defined by the Joint. A Joint removes two degreesoffreedom 
MOBILITY = Number of Motion Dimensions – Number of DegreesofFreedom When the Mobility = 0 the KinematicChain is a kinematicallydefined chain. The Target: Number of MotionDimension FBs = Number of DOF of the KinematicChain. 

The Kutzbach Criterion states that for a kinematicchain to be useful, the number of 'drives' (motiondimension) must equal the number of degreesoffreedom. 
Open Kinematic Chain
Closed Kinematic Chain
DegreesofFreedom and Mobility: with Motion DimensionsOpen Kinematic Chain
Closed Kinematic Chain
