Introduction to Robotics Kinematics

1. Introduction to Robotics Kinematics

2. Link Description

3. Kinematics Function of a link Link length Link twist

4. What are the kinematics functions of this link? a = 7  = 450

5. Link offset d Joint angle  Describe the connection between two links

6. Summary of the link parameters in terms of link frames. • ai = the distance from Zi to Zi+1 measured along Xi • i= the angle between Zi and Zi+1 measured about Xi • di = the distance from Xi-1 to Xi measured along Zi • i = the angle between Xi-1 and Xi measured about Zi • We usually choose ai > 0 since it corresponds to a distance; • However,i , di , i are signed quantities.

7. There is no unique attachment of frames to links: • 1.       When we align Zi axis with joint axis i, two choices of the Zi direction. • 2.       When we have intersecting joint axes (ai=0), two choices of the Xi direction, corresponding to choice of signs for the normal to the plane containing Zi and Zi+1. • 3.       When axes i and i+1 are parallel, the choice of origin location for {i} is arbitrary (generally chosen in order to cause di to be zero).

9. Three link Arm (RRR) • Schematic • Parallel axes • Find coordinate systems and a, , d,  of all the three accesses  

10. z is overlapping the joint’s axis • x is perpendicular to the two joint’s axis • y is …? • 0 = 1 = 2 = 0 • a0 = 0; a1 = L1; a2 = L2 • d1 = d2 = d3 = 0 • i = i

11. Three link Arm : RPR mechanism • “Cylindrical” robot – 2 joints analogous to polar coordinates when viewed from above. • Schematic: point – axes intersection; prismatic joint at minimal extension • Find coordinate systems and a, , d,  (i=3)

12. 0 = 0; 1 = 90; 2 = 0 • a0 = 0; a1 = 0; a2 = 0 • d1 = 0; d2 = d2; d3 = L2; • 1 = 1; 2 = 0; 3 = 3;

13. Schematic RRR • Parallel / Intersect (orthogonal) axes • Find coordinate systems and a, , d,  of all joints • Two possible frame assignments and corresponding parameters for the two possible choices of Z and X directions.

14. Option 1

15. Option 2

18. 0 = 0; 1 = 90; 2 = 0 • a0 = 0; a1 = 0; a2 = 0 • d1 = 0; d2 = d2; d3 = L2; • 1 = 1; 2 = 0; 3 = 3;