1 / 7

ECE 450 Introduction to Robotics

ECE 450 Introduction to Robotics. Section: 50883 Instructor: Linda A. Gee 9/28/99 Lecture 08. Transformation Matrices for End Effectors. Position. Orientation. 1 0 0 p x. 0. [ n s a ]. or R . 0 1 0 p y. T position. =.

tab
Télécharger la présentation

ECE 450 Introduction to Robotics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ECE 450 Introduction to Robotics Section: 50883 Instructor: Linda A. Gee 9/28/99 Lecture 08

  2. Transformation Matrices for End Effectors Position Orientation 1 0 0 px 0 [n s a] or R 0 1 0 py Tposition = 0 0 0 1 pz 0 0 0 0 1 0 0 0 1

  3. Euler Angle Representation of a Rotation Matrix • There are three Euler angle methods of representation • Eulerian Angles (System I) R,, =Rz, Ru, Rw, • Euler Angles (System II) R,, =Rz, Rv, Rw, • Roll, Pitch, Yaw:RPY(System III) R,, =Rz, Ry, Rx, z w v y u z x Roll  Pitch  Yaw  y x

  4. Specifications of Hand Position • The position of the hand can be specified in other coordinates • Cylindrical • Spherical

  5. 1 0 0 px 0 where 0R6 = Rotation matrix in Euler Angles, 0R6 [ n s a ], Roll, Pitch, Yaw 0 1 0 py 0T6 = 0 0 0 1 pz 0 0 0 0 1 0 0 0 1 Resultant Arm Transformation Matrix represents the arm transformation matrix and describes position and orientation of hand w.r.t. the base coordinate frame 0T6 (3x3 : orientation of hand; 3x1: location of end effector)

  6. a s n d y r  0 1 0 0 rcos 0R6 x 0 0 1 0 rsin 0T6 = 0 0 0 1 d 0 0 0 1 0 0 0 1 End Effector Position using Cylindrical Coordinates z Tcylindrical = Tz,d Tz,Tx,r px = rcos py = rsin pz = d

  7. 0 1 0 0 rcossin 0R6 0 0T6 = 0 1 0 rsinsin 0 0 0 1 rcos 0 0 0 1 0 0 0 1 End Effector Position using Spherical Coordinates z a Tspherical = Tz,Ty,Tz,r s px = rcos sin py = rsin sin pz = r cos r n  y  x

More Related