Robotics 1

Displacement Vectors

Displacement Vectors

This video introduces the concept of 'Rotation Matrices' as a way to represent the rotation, or orientation, of one coordinate frame relative to another. The three rotation matrices (rotation around X, Y, and Z) are given, and the derivation of the rotation around the Z axis shown. This video also shows how any rotations can be accomplished by stringing together rotations around X, Y, and Z, and multiplying the corresponding matrices.

This video explains displacement vectors, which express the distance between the centers of two frames.

This video gives examples of finding the displacement vectors for the five standard manipulator types.

This video shows how to enter displacement vectors in Python code.

To complete this lab activity, make a video that includes the following in one video:

Undergraduate and Graduate students:

(1) You saying your name

(2) Your Python code calculating and displaying the two displacement vectors, d0_1 and d1_2, for the 2-degree-of-freedom SCARA type manipulator

Graduate students only:

(3) Your 2-degree-of-freedom SCARA manipulator built on your board with the marker as its end-effector, moving to a position

(4) Your Python code correctly using the homogeneous transformation matrix to predict the position of the marker

Undergraduate and Graduate students:

(1) You saying your name

(2) Your Python code calculating and displaying the two displacement vectors, d0_1 and d1_2, for the 2-degree-of-freedom SCARA type manipulator

Graduate students only:

(3) Your 2-degree-of-freedom SCARA manipulator built on your board with the marker as its end-effector, moving to a position

(4) Your Python code correctly using the homogeneous transformation matrix to predict the position of the marker

This video shows how the rotation matrix and the displacement vector can be combined to form the Homogeneous Transformation Matrix. These matrices can be combined by multiplication the same way rotation matrices can, allowing us to find the position of the end-effector in the base frame. In this video, we complete calculating the Homogeneous Transformation Matrix in our Python code and test the results with the manipulator we built on our board.