### inverse - Mechanical Engineering

```MEGN 536 – Computational Biomechanics
Prof. Anthony Petrella
Musculoskeletal Modeling & Inverse Dynamics
MSM for Medical Device Design
 Musculoskeletal Modeling (MSM) may be applied to
activities of daily living (ADL) to find…
 Kinematics – potential joint motions of interest
 Muscle forces acting on skeleton
 These data may be used directly in design or applied
to lower scale models (FE) to focus on tissue level
and implant performance in situ
MSM Governing Equations
 MSM generally rigid body dynamics
 Newton-Euler equations most common,
other methods (e.g., Lagrange’s equations)
 General 3D form of Newton-Euler:
 For the 2D case (x-z plane) we can simplify to:
Inverse vs. Forward Dynamics
 You will often here ref. to
forward and inverse
dynamics in context of
MSM simulation
 Figure summarizes core
difference
 OpenSim commonly known
for forward dynamics
 AnyBody commonly known
for inverse dynamics
(Otten, 2003)
Inverse vs. Forward Dynamics
 Integrate explicitly in time to get
velocities and positions
 Stability is not guaranteed
 Differentiate wrt time to get
velocities and accel’s  forces
 Small position errors amplified by
numerical differentiation
(Hoffman, Numerical Methods for Scientists and Engineers, McGraw Hill, 1992)
MSM Inputs & Outputs (inverse)
 Inputs to a MSM simulation usually are…




Anthropometric measures (body mass, segment props)
Marker coordinates from experimental mocap system
Ground reaction force (GRF) measurements
Electromyography (EMG) traces for important muscles
 Outputs include…




All kinematics for segments and joints
Joint reaction forces at all joints
Muscle forces throughout skeleton
Interface forces between body and objects in environment
 Forces expressed as F = a * Strength, where a is
activation level in range [0,1]
Practical Difference: Forward vs. Inverse
 ID generally solves for forces in each increment of motion
independently
 FD may consider entire motion cycle and include muscle
activation / deactivation dynamics
 Not necessary for accurate simulation of many activities
100
Excitation Level
Activation Level
90
80
Control Signal (%)
70
60
50
40
30
20
(Anderson and Pandy, 2001)
10
0
0
10
20
30
40
50
60
Time (ms)
70
80
90
100
Inverse Dynamics  Essential Skill
 ID common, some FD methods even begin with ID
 Number of parameters grows quickly  software
such as AnyBody necessary for practical problems
 You will do an ID problem by hand for a simple,
2-segment arm model
 General steps…
shoulder
 Kinematics (given)
 Inverse Dynamics
 Muscle Force Calculation
hand
elbow
```