Musculoskeletal Dynamics SLate supped cal Engineerin Grant Schaffner ATA Engineering, Inc H arv ard Medical ACHU FTECHN
Musculoskeletal Dynamics Grant Schaffner ATA Engineering, Inc
What is musculoskeletal dynamics pace Biomedical Engineerin Life Support Modeling the human body and associated objects as a system of linked rigid segments Formulation of the equations of motion for this system Computational simulation of motion
What is musculoskeletal dynamics? • Modeling the human body and associated objects as a system of linked rigid segments • Formulation of the equations of motion for this system • Computational simulation of motion Z X q1 q2 q3
What is it useful for? pace Biomedical Engineerin Life Support 1. Task feasibility Range of motion studies Strength requirements (joint torques) 2. Joint forces(skeletal loading) 3. Spacesuit design(modeling suit mechanics) 4 Countermeasure evaluation 5. Understanding complex dynamics EVA tasks, e.g., Satellite capture, mass manipulation(ISS assembly /ORU replacement Artificial / reduced gravity C Video*)
What is it useful for? 1. Task feasibility • Range of motion studies • Strength requirements (joint torques) 2. Joint forces (skeletal loading) 3. Spacesuit design (modeling suit mechanics) 4. Countermeasure evaluation 5. Understanding complex dynamics • EVA tasks, e.g., Satellite capture, mass manipulation (ISS assembly / ORU replacement) • Artificial / reduced gravity (* Video *)
EVA Mass Manipulation Simulation pace Biomedical Engineerin Life Support Joint Angle Joint Torque 10 -60 -30 10 Time [sec Time [sec 30 20 10 -30 121620 8121620 Time [sec Time [sec
EVA Mass Manipulation Simulation 0 2 46 8 1 0 -80 -60 -40 -20 0 2 0 4 0 0 2 4 6 8 10 -30 -20 -10 0 1 0 2 0 3 0 0 4 8 12 20 -80 -60 -40 -20 0 2 0 4 0 0 4 8 12 16 20 -30 -20 -10 0 1 0 2 0 3 0 Joint Angle Joint Torque Time [sec] Time [sec] Time [sec] Time [sec] 1 6
Satellite Capture Simulation pace Biomedical Engineerin Life Support 0.20 1.50 X-trans Y-trans Z-trans 1.00 0.15 RolX Pitch(z) 0.10 0.05 0E235 1.00 Time(s)
Satellite Capture Simulation -0.05 0.00 0.05 0.10 0.15 0.20 02 5 8 Time (s) Linear D isplacement ( m) -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 Angular Displacement ( deg) X-trans Y-trans Z-trans Roll(X) Yaw(Y) Pitch(Z) Y X Z 1 4 3 7 6 9
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′
Coordinate Transformations pace Biomedical Engineerin Life Support Coords of pt. P wrt fixed frame O-xyz Position of p wrt coord frame fixed to rigid body, O'-xhV1Zb X=X +un+ut+wb X=X,+Rx
Coordinate Transformations • Coords of pt. P wrt fixed frame O-xyz ⎥⎥⎥⎦⎤ ⎢⎢⎢⎣⎡ = zyx x • Position of P wrt coord frame fixed to rigid body, O’-x by bz b b oo b wvu wvu Rxxx btnxxx += +++= ⎥⎥⎥⎦⎤ ⎢⎢⎢⎣⎡ = ˆ ˆ ˆ x y z nˆ tˆ bˆ b x b z b y O O ′ P x o x b x