Title: Multibody system
Content:  The degrees of freedom denote the number of independent kinematical possibilities to move. In other words, degrees of freedom are the minimum number of parameters required to completely define the position of an entity in space. A rigid body has six degrees of freedom in the case of general spatial motion, three of them translational degrees of freedom and three rotational degrees of freedom. In the case of planar motion, a body has only three degrees of freedom with only one rotational and two translational degrees of freedom. The degrees of freedom in planar motion can be easily demonstrated using a computer mouse. The degrees of freedom are: left-right, forward-backward and the rotation about the vertical axis.
Title: Degrees of freedom (mechanics)
Content:  It is common practice to design the linkage system so that the movement of all of the bodies are constrained to lie on parallel planes, to form what is known as a planar linkage. It is also possible to construct the linkage system so that all of the bodies move on concentric spheres, forming a spherical linkage. In both cases, the degrees of freedom of the links in each system is now three rather than six, and the constraints imposed by joints are now c = 3 − f. In this case, the mobility formula is given byAn example of a planar simple closed chain is the planar four-bar linkage, which is a four-bar loop with four one degree-of-freedom joints and therefore has mobility M = 1.
Title: Mechanism (engineering)
Content:  While all mechanisms in a mechanical system are three-dimensional, they can be analysed using plane geometry if the movement of the individual components is constrained so that all point trajectories are parallel or in a series connection to a plane. In this case the system is called a planar mechanism. The kinematic analysis of planar mechanisms uses the subset of Special Euclidean group SE, consisting of planar rotations and translations, denoted by SE. The group SE is three-dimensional, which means that every position of a body in the plane is defined by three parameters. The parameters are often the x and y coordinates of the origin of a coordinate frame in M, measured from the origin of a coordinate frame in F, and the angle measured from the x-axis in F to the x-axis in M. This is often described saying a body in the plane has three degrees of freedom. The pure rotation of a hinge and the linear translation of a slider can be identified with subgroups of SE, and define the two joints one degree-of-freedom joints of planar mechanisms. The cam joint formed by two surfaces in sliding and rotating contact is a two degree-of-freedom joint.
Title: Degrees of freedom
Content:  Degrees of freedom (mechanics) describes the number of independent motions that are allowed to a body. In the case of a mechanism made of several bodies, it refers to the number of possible independent relative motions between the pieces of the mechanism. Ball-and-socket joints, such as the human wrist or hip, can freely rotate and have three degrees of freedom. A free, rigid object, such as a ship at sea, has six degrees of freedom: three rotations and three translations about each perpendicular axis. In the study of complex motor control, there may be so many degrees of freedom that a given action can be achieved in many different ways. The brain must select and combine movements with different degrees of freedom. This issue is sometimes called the degrees of freedom problem.
Title: Degrees of freedom (mechanics)
Content:  In physics, the degrees of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration or state. It is important in the analysis of systems of bodies in mechanical engineering, structural engineering, aerospace engineering, robotics, and other fields. The position of a single railcar (engine) moving along a track has one degree of freedom because the position of the car is defined by the distance along the track. A train of rigid cars connected by hinges to an engine still has only one degree of freedom because the positions of the cars behind the engine are constrained by the shape of 
Title: Linkage (mechanical)
Content:   It is common practice to design the linkage system so that the movement of all of the bodies are constrained to lie on parallel planes, to form what is known as a planar linkage. It is also possible to construct the linkage system so that all of the bodies move on concentric spheres, forming a spherical linkage. In both cases, the degrees of freedom of the link is now three rather than six, and the constraints imposed by joints are now c = 3 − f. In this case, the mobility formula is given by  An example of a planar simple closed chain is the planar four-bar linkage, which is a four-bar loop with four one degree-of-freedom joints and therefore has mobility M = 1.
Title: Kinematic chain
Content:  The degrees of freedom, or mobility, of a kinematic chain is the number of parameters that define the configuration of the chain. A system of n rigid bodies moving in space has 6n degrees of freedom measured relative to a fixed frame. This frame is included in the count of bodies, so that mobility does not depend on link that forms the fixed frame. This means the degree-of-freedom of this system is M = 6(N − 1), where N = n + 1 is the number of moving bodies plus the fixed body. Joints that connect bodies impose constraints. Specifically, hinges and sliders 
Title: Mechanism (engineering)
Content:  one degree of freedom. ; A cylindrical joint requires that a line in the moving body remain co-linear with a line in the fixed body. It combines a revolute joint and a sliding joint. This joint has two degrees of freedom. ; A spherical joint, or ball joint, requires that a point in the moving body maintain contact with a point in the fixed body. This joint has three degrees of freedom. ; A planar joint requires that a plane in the moving body maintain contact with a plane in a fixed body. This joint has three degrees of freedom. ; A screw joint, or helical joint, has only one degree of freedom because the sliding and rotational motions are related by the helix angle of 
Title: Degrees of freedom (mechanics)
Content: 1) For a single particle in a plane two coordinates define its location so it has two degrees of freedom; ; 2) A single particle in space requires three coordinates so it has three degrees of freedom; ; 3) Two particles in space have a combined six degrees of freedom; ; 4) If two particles in space are constrained to maintain a constant distance from each other, such as in the case of a diatomic molecule, then the six coordinates must satisfy a single constraint equation defined by the distance formula. This reduces the degree of freedom of the system to five, because the distance formula can be used to solve for the remaining coordinate once the other five are specified. The position of an n-dimensional rigid body is defined by the rigid transformation, [T] = [A, d], 
Title: Chebychev–Grübler–Kutzbach criterion
Content:  It is common practice to design the linkage system so that the movement of all of the bodies are constrained to lie on parallel planes, to form what is known as a planar linkage. It is also possible to construct the linkage system so that all of the bodies move on concentric spheres, forming a spherical linkage. In both cases, the degrees of freedom of the links in each system is now three rather than six, and the constraints imposed by joints are now c = 3 − f. In this case, the mobility formula is given byAn example of a planar simple closed chain is the planar four-bar linkage, which is a four-bar loop with four one degree-of-freedom joints and therefore has mobility M = 1.

Question: number of degree of freedom for plane mechanism?
Answer: six.
two.