Technique/ Limitations pace Biomedical Engineerin Life Support Use the simplest possible model that adequately describes the dynamics of interest Use open kinematic chains Individual segments are rigid bodies
Technique / Limitations • Use the simplest possible model that adequately describes the dynamics of interest • Use open kinematic chains • Individual segments are rigid bodies
Notes pace Biomedical Engineerin Life Support Reference Text H. Asada and J.-J. E Slotine, " Robot Analysis and Control, John Wiley& Sons, 1986 Nomenclature Vectors or matrices are denoted by bold script(X, R) Scalar values are denoted by regular script(x, 0)
Notes Reference Text • H. Asada and J.-J. E. Slotine, “Robot Analysis and Control”, John Wiley & Sons, 1986 Nomenclature • Vectors or matrices are denoted by bold script ( • Scalar values are denoted by regular script ( x R x θ ), )
pace Biomedical Engineerin Life Support Part Musculoskeletal Kinematics
Part I Musculoskeletal Kinematics
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′