Module 2 : Robots mechanisms
Lecture 5 : Manipulators Mechanisms-I
Degrees Of Freedom
 

It is required to find DOF for a manipulator which in turn decides the number of actuators required. The task is relatively straightforward for open chains –serial manipulators. In most of these, the chain is composed of links connected through revolute or prismatic pairs. The degrees of freedom simply turn out to be the number of moving links in the open chain - and the number of actuators will equal the degrees of freedom. The word “axis” is often used instead of degrees of freedom. Thus a manipulator with six moving links and as many revolute pairs is called a 6-axis manipulator. Note that the actuator used to power the gripper (open and close fingers etc) is not counted as an “axis” – since the function of the actuator on the gripper is solely to open and close the fingers. Also, the actuator for the gripper does not contribute to the positioning and orienting capability of the end-effector.

 

Closed chains.

 

Figure 5.1.1
 

To find the DOF of mechanism in robot, Gubler's formula for closed chains or given set of n links is applied.

1.

For the 5R mechanism shown above Figure 5.1.1, let
Jr- no of revolute joints; Jp – no of prismatic joints
Then Gublers formula states that DOF=3(n-1)-2Jr-2Jp
For above mechanism of 5R; DOF=3(5-1)-2x5=2

2.

For 4RP mechanism, n=5, Jr=4, Jp=1 therefore DOF= 3(5-1)-2x4-2x1=2

 

Figure 5.1.2
3.

Figure 5.1.2 for 6R bar planer mechanism n=6, Jr= 6, Jp=0
Therefore Mechanism DOF = 3(6-1)-2x6=15-12=3

 

Work space of closed chains will be less than that of open chains.