Great videos!
http://see.stanford.edu/see/lecturelist.aspx?coll=86cc8662-f6e4-43c3-a1be-b30d1d179743
http://en.wikipedia.org/wiki/Denavit%E2%80%93Hartenberg_parameters
Dot Product
4 by 4 Rotation matrix
http://www.cprogramming.com/tutorial/3d/rotationMatrices.html
http://see.stanford.edu/materials/aiircs223a/handout2_Kinematics-1.pdf
http://see.stanford.edu/materials/aiircs223a/handout3_Kinematics-2.pdf
Euler rotation theorem
http://vectoralgebra.info/axisangle.html
The axis-angle representation is equivalent to the more concise rotation vector, or Euler-Rodrigues vector representation. In this case, both the axis and the angle are represented by a non-normalized vector codirectional with the axis whose magnitude is the rotation angle. From an orientation matrix R the Axis-Angle parameters can be calculated as:
It is equivalent to the Euler-Rodrigues vector representation, where the vector v is defined as the product e = theta.u
For a Rotation matrix: