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 [General] Parts free to move in space have six[6] degreesoffreedom [D.O.F.]. Why six? Take the image to the left, you can see that a Part, in general 'Global Coordinates:


DOF of a FreePart on a MechanismPlane In MechDesigner, Parts lie on a MechanismPlane. A FreePart has three[3] D.O.F. The Part can translate along the: x and y directions. The Part can rotate about axis that is normal to the MechanismPlane: θ 
PinJoint: Requires a Line in the moving Part to remain colinear with a Line in the MechanismPlane, and a plane perpendicular to this Line in the moving Part maintain contact with a similar perpendicular plane in the MechanismPlane. A PinJoint removes two degreesoffreedom  the Part has one degreeoffreedom remaining  it can rotate. 

SlideJoint Requires that a Line in the moving Part remains colinear with a line in the MechanismPlane, and a plane parallel to this Line in the moving Part maintain contact with a similar parallel plane in the MechanismPlane. A SlideJoint removes two degreesoffreedom  the Part has one degreeoffreedom remaining  it can slide. 
DOF of a KinematicChain? Kinematicchains may have many Parts and Joints. Fortunately, we can use the Gruebler Equation to calculate the number of degreesoffreedom of most kinematicchains. 

Gruebler Equation For a Planar kinematicchain, the Gruebler Equation is: F = 3*(N1) – 2*J – H MechDesigner automatically calculates the number of DegreesofFreedom in a KinematicChain. Note: if the DegreesofFreedom = Zero, then the kinematicchain is a structure. 
where: F = degreesoffreedom for the kinematicchain N = number of parts  include the BasePart J = number of one degreeoffreedom joints H = number of 'higherpair' joints  see Joints 
It is important to notice that the Gruebler Equation does not need to know the lengths or shape of parts or the type of joint. 
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 D.O.F. in the KinematicChain. 

The Kutzbach Criterion states that for a kinematicchain to be useful, the number of 'drives' (motiondimension) must equal the number of degreesoffreedom. 
DegreesofFreedom and Mobility: without Motion Dimensions Open Kinematic Chain
Closed Kinematic Chain
DegreesofFreedom and Mobility: with Motion Dimensions Open Kinematic Chain
Closed Kinematic Chain
