Lecture 16
16-311 Introduction to Robotics
Prof. Howie Choset

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Denavit Hartenberg Notes:

• Assigning coordinate systems:
  • Assign Z_i along the axis of joint i.
    • For a revolute joint, the joint axis is along the axis of rotation.
    • For a prismatic joint, the joint axis is along the axis of translation.
  • Choose X_i to point along the common perpendicular of Z_i and Z_i+1 pointing towards the next joint.
    • if Z_i and Z_i+1 intersect, then choose X_i to be normal to the plane of intersection.
  • Choose Y_i to round out a right hand coordinate system.
    • The Y-axis is not used for Denavit Hartenberg so it is usually not drawn in the interest of less clutter.
• DH parameters
  • a_i-1: distance from Z_i-1 to Z_i along X_i-1
  • : angle from Z_i-1 to Z_i about X_i-1
  • d_i: distance from X_i-1 to X_i along Z_i
  • : angle from X_i-1 to X_i about Z_i

Transformation Matrix from DH parameters: Denavit Hartenberg examples:

• Example 1: Rotation CCW is pos, Rotation Clockwise with X into the paper is Rotation CCW, joint variables about Z axis
  
• Example 2: Wrist has 3 DOF that meet at a common origin