Position and Orientation of Rigid Body & pace Biomedical Engineerin Life Support Position of rigid body is represented with reference to coord frame O-xyz by b Represent orientation of rigid body yb ith coord frame O'xhvhZb Components of unit vectors are direction cosines of each axis Combine the three unit vectors into a3x3matrⅸx.R.the“ Rotation matrix” (orthonormal matrix) R=n,t, b]Position and Orientation of Rigid Body • Position of rigid body is represented with reference to coord frame O-xyz by ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = o o o o z y x x ]ˆ = ,ˆ[ ˆ,btnR • Represent orientation of rigid body with coord frame O’-xbybzb • Components of unit vectors are direction cosines of each axis • Combine the three unit vectors into a 3x3 matrix, R, the “Rotation Matrix” (orthonormal matrix) x y z nˆ tˆ bˆ b x b z b y O O′