Degrees of freedom for the robots 1.pptx

Robots

1. Degree of Freedom 'Degree of Freedom' ( DoF ) : Is related to robotic arms, Is an independent joint that can provide freedom of movement for the manipulator, either in a rotational or translational (linear) sense. Every geometric axis that a joint can rotate around or extend along is counted as a Single Degree of Freedom. Is widely used to define the motion capabilities of robots. G enerally refers to  the number of joints or axes of motion on the robot . Is needed to uniquely define position of a system in space at any instant of time.

2. The six degrees of freedom: forward/back, up/down, left/right, yaw, pitch, roll

3. Degree of Freedom of mechanisms and structures The degree of freedom of an assembly of links completely predicts its character. There are only three possibilities. 1- If the DOF is positive , it will be a mechanism, and the links will have relative motion. 2- If the DOF is exactly zero , then it will be a structure, and no motion is possible. 3- If the DOF is negative , then it is a preloaded structure, which means that no motion is possible and some stresses may also be present at the time of assembly.

4. m = 3 N = 4 links J = 4 joints D O F = 3( 4 − 1 − 4 ) + 4 DOF = 1

5. Degree of Freedom (DoF): m = 3 N = 5 links J = 5 joints D O F = 3(5 − 1 − 5) + 5 DOF = 2

6. Degree of Freedom (DoF): m = 3 N = 5 links J = 4 joints DoF = 3(5 − 1 − 4) + 4 DoF = 4 Redundant robot

7. m = 3 N = 6 links J = 7 joints DoF = 3(6 − 1 − 7) + 7 DoF = 1

8. m = 3 N = 6 links J = 7 joints DoF = 3(6 − 1 − 7) + 7 DoF = 1

9. Degree of Freedom (D O F): Three links are connected at a single point A. Since a joint connects exactly two links, the joint at A is correctly interpreted as two revolute joints overlapping each other . Mechanism with two overlapping joints m = 3 N = 8 links J = 9 joints DoF = 3(8 − 1 − 9) + 9 DoF = 3

10. m = 3 N = 4 links J = 4 joints DoF = 3(4 − 1 − 4) + 4 DoF = 1 Slider- crank mechanism The fixed link connected with the slider is considered as ground.

11. Degree of Freedom (DOF):

12. m = 3 N = 7 links J = 9 joints DoF = 3(7 − 1 − 9) + 9(1) DoF = 3

13. Degree of Freedom (DoF): Parallel Robots: However, only three DoF are visible at the end effector that moves parallel to the fixed platform. So, the Delta robot acts as an x − y − z Cartesian positioning device . Delta robot Dr. Haitham El- Hussieny m = 6 N = 17 links J = 21 joints DoF = 6(17 − 1 − 21) + 9(1) + 12(3) DoF = 15

14. m = 6 N = 14 links J = 18 joints ( 6 × P , 6 × U , 6 × S ) D O F = 6(14 − 1 − 18) + 6(1) + 6(2) + 6(3) D O F = 6 Stewart- Gough platform Dr. Haitham El- Hussieny The Stewart-Gough platform is a popular choice for car and airplane cockpit simulators since it moves with the full six degrees of freedom of motion of a rigid body. Its parallel structure means that each leg needs to support only a fraction of the weight of the payload. Degree of Freedom (DOF):

15. m = 3 N = 5 links J = 4 joints D O F = 3(5 − 1 − 4) + 4 D O F = 4 m = 6 N = 6 links J = 5 joints D O F = 6(6 − 1 − 5) + 5 D O F = 5 Degree of Freedom (DOF):

16. Using Gr u ¨ ebler’s equation, t his linkage has zero degrees of freedom: DoF = 3(5 − 1 − 6) + 6(1) = This indicates that the mechanism is locked (No motion). This is true if all pivoted links are not identical . If all pivoted links were the same size and the distance between the joints on the frame and coupler were identical, this mechanism is capable of motion, with a single degree of freedom . The center link is redundant and because it is identical in length to the other two links attached to the frame, it can be removed and, DoF = 3(4 − 1 − 4) + 4(1) = 1 A parallelogram linkage N = 5 , J = 6 R Dr. Haitham El- Hussieny Degree of Freedom (DOF):

17. Degree of Freedom (DOF): Important Note: Grübler’s equations is obviously useful in determining the mobility of a wide variety of commonly used engineering mechanisms.. BUT it yields theoretical results, and can be easily misleading because it does not take geometry into account. Therefore, when an ambiguous result is obtained, the actual mobility of a mechanism must be determined by inspection.