The purpose of this tutorial is to demonstrate how OpenSim solves an inverse kinematics problem and an inverse dynamics problem using experimental data. To diagnose movement disorders and study human movement, biomechanists frequently ask human subjects to perform movements in a motion capture laboratory and use computational tools to analyze these movements. A common step in analyzing a movement is to compute the joint angles and joint moments of the subject during movement. OpenSim has tools for computing these quantities:

1. Inverse kinematics is used to compute joint angles.

2. Inverse dynamics is used to compute net joint reaction forces and net joint moments.

Inverse kinematics computes the joint angles for a musculoskeletal model that best reproduce the motion of a subject. Inverse dynamics then uses joint angles, angular velocities, and angular accelerations of the model, together with the experimental ground reaction forces and moments, to solve for the net reaction forces and net moments at each of the joints. The schematic below shows an overview of the inverse kinematics and inverse dynamics problems.

In this tutorial, you will:

• Become familiar with OpenSim's Scale, Inverse Kinematics and Inverse Dynamics tools

• Solve an inverse kinematics and inverse dynamics problem using experimental data

• Interpret the results of the inverse dynamics solution

• Investigate the dynamic inconsistencies that arise during inverse dynamics

Each section of the tutorial guides you in using certain tools within and asks you to answer a few questions. The menu titles and option names you must select and any commands you must type to run OpenSim will appear in bold face. The questions can be answered based on information from OpenSim and basic knowledge of the human musculoskeletal system. After you complete the tutorial, feel free to explore OpenSim and the other analysis tools further on your own. Depending on the amount of exploration you do, this tutorial should take 1-2 hours to complete.

In this tutorial, you will be using a generic musculoskeletal model with 23 degrees of freedom and actuated by 54 muscles entitled 3DGaitModel2354. It is a simplified version of the lower-extremity model of Delp et al. [1], modified to include a torso and back joint based on the model of Anderson and Pandy [2].

To load the generic musculoskeletal model into OpenSim:

• Click the File menu and select Open Model.

• Find the Models folder, which is located under your OpenSim installation directory, e.g., C:\OpenSim3.2. (The actual directory name depends on version used and can be changed during installation).

• Open the Gait2354_Simbody folder, select the file gait2354_simbody.osim, and click Open.

The experimental gait data were collected by Jill Higginson and Chand John in the Neuromuscular Biomechanics Lab at the University of Delaware as part of the study cited below. The data include marker trajectories and ground reaction forces for an adult male walking at a self-selected speed on an instrumented split-belt treadmill. Please note that the data distributed with OpenSim is from a different subject than the one described in the paper. Data collection protocols were the same for both subjects.

Chand T. John, Frank C. Anderson, Jill S. Higginson & Scott L. Delp (2012): Stabilisation of walking by intrinsic muscle properties revealed in a three-dimensional muscle-driven simulation, Computer Methods in Biomechanics and Biomedical Engineering.

The purpose of scaling a generic musculoskeletal model is to modify the anthropometry, or physical dimensions, of the generic model so that it matches the anthropometry of a particular subject. Scaling is one of the most important steps in solving inverse kinematics and inverse dynamics problems because these solutions are sensitive to the accuracy of the scaling step. In OpenSim, the scaling step adjusts both the mass properties (mass and inertia tensor), as well as the dimensions of the body segments. Scaling can be performed using a combination of two methods:

To scale the generic model: 

• Click the Tools menu and select Scale Model.

• At the bottom of the Scale Tool dialog, click Load to input a settings file.

• In the file browser, ensure that you are in the Gait2354_Simbody folder, select the file subject01_Setup_Scale.xml and click Open.

This xml file contains pre-configured settings to scale the generic musculoskeletal model to the dimensions of the subject. Notice all of the textboxes in the dialog were filled in appropriately.

1. Based on information in the Scale Tool dialog, what is the mass of the generic musculoskeletal model? What was the mass of the subject?

2. To see the loaded scale factors, click on the Scale Factors tab. Which body segments were scaled manually?

3. Based on information in the Inverse Kinematics Tool dialog, at what frequency was the experimental motion data captured? Hint: Look for the box titled Marker Data.

To complete the scale step:

• In the Scale Tool dialog, click Run. Then click Close.

• To save the scaled model, click File and select Save Model.

• Ensure that you are in the Gait2354_Simbody folder, type gait2354_scaled.osim into the File name textbox, and click Save.

When complete, a new, scaled model entitled subject01 will appear in View window. Notice the pink markers around the new model. The blue spheres graphically represent the experimental markers from the motion capture data used in the measurement-based scaling. 

At this point, you may close the generic model (right-click the model name in the Navigator window, and select "close") or hide the model (right-click the model name, and select Display >> Hide).

Kinematics is the study of motion without considering the forces and moments that produce that motion. Thus, to perform kinematical analyses, such as inverse kinematics, mass and inertia properties are not needed. The purpose of inverse kinematics is to find the joint angles of the model that best reproduce the experimental kinematics of a particular subject. In this tutorial, the experimental kinematics used by the inverse kinematics tool are based on experimental marker positions.

The inverse kinematics tool goes through each time step, or frame, of recorded motion and computes the set of joint angles that put the model in a configuration that "best match" the experimental kinematics. OpenSim determines this "best match" by solving a weighted least squares optimization problem with the goal of minimizing marker error. For more information about optimization and least-squares problems, see Chapter 1 of Convex Optimization by Stephen Boyd and Lieven Vandenberghe (http://www.stanford.edu/~boyd/cvxbook/).

Marker error is defined as the distance between an experimental marker and the corresponding virtual marker. Each marker has an associated weighting value, specifying how strongly that marker's error term should be minimized in the least squares problem. In each frame, the inverse kinematics tool solves for a vector of generalized coordinates (e.g., joint angles), q, that minimizes the weighted sum of marker errors, which is expressed as

where q is the vector of generalized coordinates (e.g., joint angles), x_i^exp is the position of experimental marker i, x_i(q) is the position of the corresponding virtual marker i (which depends on q), and w_i is the weight associated with marker i.

To solve the inverse kinematics problem:

• Click the Tools menu and select Inverse Kinematics.

• In the Inverse Kinematics Tool dialog, click Load to load an Inverse Kinematics setup file.

• In the file browser, ensure that you are in the Gait2354_Simbody folder, select the file subject01_Setup_IK.xml and click Open.

This xml file contains pre-configured settings to solve the inverse kinematics problem for the scaled model. Notice all of the textboxes in the dialog were filled in appropriately.

4. Click the Weights tab and scroll through the list of markers in the top half of the dialog. Which markers have weighting values less than one? Why?
Hint: Think about joints that have not been modeled.

To complete inverse kinematics step:

• In the Inverse Kinematics Tool, click Run. Then click Close.
  Note: Even though you closed the dialog, the Inverse Kinematics tool is still running. Notice the progress bar in the lower right-hand corner of the program. Wait until the bar disappears before proceeding. 

The model will begin to move slowly, as the inverse kinematics problem is being solved for each frame of the experimental data.

To compare experimental marker data with inverse kinematics results, in the Navigator panel, go to Motions and right-click on Results (which are what the Inverse Kinematics Tool just generated). Then choose Associate Motion Data... from the drop down menu. Choose subject_01_walk1.trc and click Open. Model markers are virtual markers shown in pink and experimental markers are shown in blue. Hit play in the Motion Toolbar. The virtual markers should correspond closely to the experimental marker locations as the animation proceeds.
^*Note: If using a Virtual Machine on a Mac, Command + Ctrl + Left Click on each motion.

When completed, examine the accuracy of the inverse kinematics solution:

• Click the Window menu and select Messages.

• The Messages window records details of the all steps you have performed. Take a minute to explore the Messages window. Then, scroll to the very bottom.

• The next to last line provides the markers errors and model coordinate errors (e.g., joint angle errors) associated with the last frame of the motion.
  Note: All marker errors have units in meters, and all coordinate errors have units in radians.