Robotics Coordinate Frames TEMPUS IV Project 158644 JPCR

Robotics Coordinate Frames TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS

Drawing 3 Dimensional Frames in 2 Dimensions • Y points to the right • Z points up • X points ? ? ? TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 2

Two views of the same cube Viewed from below TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS Viewed from above ROBOTICS 3

Now Overlay the 3 -D Coordinate Frame z z y y x x Viewed from below X points away from you! Viewed from above X points towards you! 4

We will always use a right-handed coordinate frame (x points out) z y x TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 5

We will not use a left-handed coordinate frame (x points in) z x TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS y ROBOTICS 6

Right Handed Coordinate Systems: Using the right hand rule • Given two axes, determine the direction of the third axis • Point right fingers along x • Curl fingers towards y • Thumb points to z TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 7

Right Handed Coordinate Systems: Using the right hand rule • Given two axes, determine the direction of the third axis z x x y TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS x y y ROBOTICS 8

Right Handed Coordinate Systems: Practice y z x x y y z y x z TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 9

Rotating Axes: Direction of Positive Rotation • If we want to rotate a frame, which way do we rotate it? • Example: Rot z (90 degrees) z x y z z y x x y TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 10

Rotating Axes: Another Right Hand Rule • Point right thumb in direction of axis you want to rotate • Fingers curl in direction of positive rotation z z Rot z (90) x y y TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS x ROBOTICS 11

Plotting Points (Neatly) in 3 -D • Example: Plot (5, 3, 4) • Step 1: Draw tick marks TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 12

Plotting Points (Neatly) in 3 -D • Example: Plot (5, 3, 4) • Step 2: Draw two lines on the groundplane 5 3 4 3 5 TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS 3 ROBOTICS 13

Plotting Points (Neatly) in 3 -D • Example: Plot (5, 3, 4) • Step 3: Draw a perpendicular with tick marks, and your point 5 5 3 4 4 3 5 TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS 4 3 ROBOTICS 14

Plotting Points: Example • Plot (1, 3, 5) on a coordinate frame where: – X points up and Y points into the paper – Y points down and Z points out of the paper TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 15

Working with Multiple Coordinate Frames Tower Coordinates TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS Plane Coordinates ROBOTICS 16

Working with Multiple Coordinate Frames • Location of the nose of the plane in tower coordinates? • Location of the origin of the tower in plane coordinates? • Location of the nose of the plane in plane coordinates? 5 m 50 meters TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 17

Working with Multiple Coordinate Frames • Location of the nose of the plane in tower coordinates? • Location of the origin of the tower in plane coordinates? • Location of the nose of the plane in plane coordinates? TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 18

Literature / references: 1) Jennifer Kay, Rowan: Introduction to Homogeneous Transformations & Robot Kinematics, University Computer Science Department, January 2005 (added material) 2) J. M. Selig: Introductory Robotics, Prentice Hall, 1992: - Chapter 3, Robot Anatomy, pp. 23 -33. 3) http: //www. powershow. com/view/11 ba 98 OTFi. M/EEE 30088005_Industrial_automation_Robotics_flash_ppt _presentation TEMPUS IV Project: 158644 – JPCR Development of Regional Interdisciplinary Mechatronic Studies - DRIMS ROBOTICS 19