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.