The Kutzbach criterion, which is similar to Gruebler’s equation, calculates the mobility. In order to control a mechanism, the number of independent input motions. Mobility Criteria in 2D. • Kutzbach criterion (to find the DOF). • Grübler criterion (to have a single DOF). F=3(n-1)-2j. DOF. # of bodies # of full. The degrees of freedom (DOF) of a rigid body is defined as the number of independent movements it has Figure shows a rigid body in a plane.1 Degree.. .

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The two lost degrees of freedom are translational movements along the x and y axes. Therefore, a revolute pair removes five degrees of freedom in spatial mechanism.

Two rigid bodies that are part of this kind of system will have an independent translational motion along the axis and a relative rotary motion around the axis. The term kinematic pairs actually refers to kinematic constraints between rigid bodies. Criteroin corresponding matrix operator, the screw operatorcritfrion a concatenation of the translation operator in Equation and the rotation operator in Equation In Figure c, a rigid body is constrained by a higher pair.

It has two degrees of freedom: Views Read Edit View history. Specifically, hinges and sliders each impose five constraints and therefore remove five degrees of freedom. These pairs reduce the number of the degrees of freedom. Figure A revolute pair R-pair A revolute pair keeps the axes of two rigid bodies together.


A mechanism is a constrained rigid body system in which one of the bodies is the frame. To determine the DOF of this body we must consider how many distinct ways the bar can be moved.

We can describe this motion with a translation criferion T We will discuss more on this topic for planar mechanisms in the next section. Figure a is an application of the mechanism.

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In two dimensions, it has one degree of freedom, translating along the x axis. Figure A lutzbach pair S-pair A spherical pair keeps two spherical centers together. Suppose the rotational angle of the point about u isthe rotation operator will be expressed by where u xu yu z are the othographical projection of the unit axis u on xyand z axes, respectively.

This composition of this rotational transformation and this translational transformation is a screw motion. It has one degree of freedom, turning around point A.

Chebychev–Grübler–Kutzbach criterion

Adding kinematic constraints between rigid bodies will correspondingly decrease the degrees of freedom of the rigid body system. Figure A prismatic pair P-pair A prismatic pair keeps two axes of two rigid bodies align and allow no relative rotation.

In this example, the body has lost the ability to rotate about any axis, and it cannot move along the y axis. Figure Iutzbach cylindrical pair C-pair A cylindrical pair keeps two axes of two rigid bodies aligned. That is, you just push or pull rod 3 to operate the window. However, the rotation z is still a variable.

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Chebychev–Grübler–Kutzbach criterion – Wikipedia

Two rigid bodies connected by this kind of pair will have two independent translational motions in the plane, and a rotary motion around the axis that is perpendicular to the plane.

There are two important special cases: The mobility formula counts the number of parameters that define the positions of a set of rigid bodies and then reduces this number by the constraints that are imposed by joints connecting these bodies.

Figure Degrees of freedom of a rigid body in space 4. Imagine that the roller is welded to link 2 when counting the degrees of freedom for the mechanism. Therefore, a screw pair removes five degrees of freedom in spatial mechanism. Therefore, a prismatic pair removes five degrees of freedom in spatial mechanism.

Therefore, a cylindrical pair removes four degrees of freedom from spatial mechanism.