Lecture on Denavit-Hartenberg Parameters

Introduction

• Denavit-Hartenberg (D-H) parameters are used to describe the motion of a series of robotic joints.
• Essential for efficient calculation of forward and inverse kinematics.

Defining Axes

1. Z-Axis:
   • For revolute joints: along the axis of rotation.
   • For prismatic joints: along the axis of translation.
2. X-Axis:
   • For the first joint: free to choose.
   • For later joints: points away from the previous joint.
3. Y-Axis:
   • Completes the right-handed reference frame.

Adding Another Joint

• Z-Axis for the new joint: along the axis of rotation.
• Common Normal: Orthogonal to both Z-axes (shortest line between them).
• X-Axis: Points along the common normal; origin at the intersection of the new Z-axis.
  • Note: D-H parameters focus on the motion of links, not physical component placement.

Four Parameters

1. d: Depth along the previous joint's Z-axis from the origin to the common normal.
2. Theta (θ): Rotates about the previous Z-axis to align the X-axis.
3. r / a: Length of the common normal; also radius of revolution for the new origin about the previous Z-axis.
4. Alpha (α): Rotates about the new X-axis to align Z with the joint motion axis.

Special Case: Parallel Z-Axes

• Z-Axes Parallel: Infinite number of common normals.
• Choosing d: Any D value to place the origin at a convenient location (center of the link or end effector tip).
• Theta (θ): Rotates about Z to align the X-axis with the normal.
• r / a: Translates along the normal to reach the new origin.
• Alpha (α): 0 (no rotation needed).

Conclusion

• Denavit-Hartenberg Parameters: Simplifies the layout of reference frames and transformations between joints. **