Forward kinematics - Revolute matrices

Question 1

Direction cosine matrix.

Answer 1

Is a transformation matrix that transforms one coordinate reference frame to another.

Question 2

What is a revolute (rotation) matrix?

Answer 2

Is a transformation matrix that is used to perform a rotation in Euclidean space.

Question 3

Elementary revolute (rotation) matrices.

Answer 3

…

Question 4

Direction cosine matrix to revolute matrices. Draw some sketches.

Answer 4

1. Ref. frames with same origin
2. P1 = R2,1 * P2
3. Elementary matrices
4. Euler / Cardan angles

Question 5

Revolute matrices properties.

Answer 5

• Inverse
• Composition

Question 6

What are the aeronautical angles?

Answer 6

• Cardan angles: Z Y’ X’’
• Euler angles: Z Y’ Z’’

Question 7

Steps for rotating a reference frame in order to obtain a fixed one (using Cardan angles).

Answer 7

1. Rz -> goal of putting Y’ perpendicular to X’’
2. Ry -> goal of putting X’’ in the final position
3. Rx -> goal of adjusting the orientation of the other 2 axis