Degrees of Freedom (DOF) or Mobility

• DOF: Number of independent parameters(measurements) needed to uniquely define the position of a system in space at any instant of time.

• A mechanical system’s mobility (M) can be classified according to the number of degrees of freedom (DOF).

• DOF is defined with respect to a selected frame of reference (ground).

 Rigid body in a plane has 3 DOF: x,y,z

 Rigid body in 3D-space has 6 DOF, 3 translations & 3 rotations

three lengths (x, y, z), plus three angles(θ, φ, ρ).

 The pencil in these examples represents a rigid body or link.

Types of Motion

• Pure rotation: the body possesses one point (center of rotation) that has no motion with respect to the

“stationary” frame of reference. All other points move in circular arcs.

• Pure translation: all points on the body describe parallel (curvilinear or rectilinear) paths.

• Complex motion: a simultaneous combination of rotation and translation.

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