CALCULATE DEGREE OF FREEDOM MECHANICS PLUS

The next mechanism is called a four-bar linkage, obtained by pinning the endpoint of the 3R robot to a particular location in the plane. The robot has 3 degrees of freedom, as we expect. This planar robot has, m=3, N=4, J=3, and one freedom at each joint. It's called a 3R robot, meaning it has three revolute joints.

The first mechanism is called a serial, or open-chain, robot, because there is a single path from ground to the end of the robot. Let's apply Grubler's formula to a few mechanisms. This is called Grubler's formula, and it assumes that the constraints provided by the joints are independent. Since the number of constraints provided by joint i is equal to m minus the number of freedoms allowed by joint i, we can replace ci by m minus fi and rewrite the equation like this. Then we subtract off the constraints provided by the J joints. We can write our equation in terms of these variables: N-1 is the number of links other than ground, and m times N-1 is the total number of freedoms of the bodies if they are not constrained by joints. And we define m to be the degrees of freedom of a single body, so m equals 3 for a rigid body moving in the plane and m equals 6 for a rigid body moving in 3-dimensional space. By historical convention, N includes ground as a link. Using this table of freedoms and constraints provided by joints, we can come up with a simple expression to count the degrees of freedom of most robots, using our formula from Chapter 2.1. This table shows the number of degrees of freedom of each joint, or equivalently the number of constraints between planar and spatial bodies.

CALCULATE DEGREE OF FREEDOM MECHANICS PLUS

This table summarizes the previous four joints, plus two other types of joints, the one-degree-of-freedom helical joint and the two-degree-of-freedom cylindrical joint. The spherical joint, also called a ball-and-socket joint, has three degrees of freedom: the two degrees of freedom of the universal joint plus spinning about the axis. We can also have joints with more than one degree of freedom, like this universal joint, which has two degrees of freedom. It places 5 constraints on the motion of the second spatial rigid body relative to the first, and therefore the second body has only one degree of freedom relative to the first body, given by the angle of the revolute joint.Īnother common joint with one degree of freedom is the prismatic joint, also called a linear joint. The most common type of joint is the revolute joint. The constraints on motion often come from joints. In the previous video, we learned that the number of degrees of freedom of a robot is equal to the total number of freedoms of the rigid bodies minus the number of constraints on their motion.

Calculate degree of freedom mechanics