Force-Dependent Kinematics
The usual mode of operation of AnyBody is such that we input some observed or assumed motions to our model, and the software proceeds to compute the internal forces. This is also called inverse dynamics, and it links directly back to Newtons second law, which in its simplest form for a particle reads:
F = m a
where F is the vector of resulting forces acting on the system, m is the mass, and a is the vector of acceleration of the particle. This law basically allows us to determine the forces if we know the acceleration (i.e. the motion) or determine the motion if we know the forces.
AnyBody usually takes motion as input and computes forces as output, because it is easy to observe motion visually or with motion capture systems, while internal forces in a biomechanical system are very difficult to know anything about. This is standard inverse dynamic analysis.
AnyBody is a rigid body dynamics system. In other words, it presumes that the segments in the system do not deform and it, therefore, solves not only Newton's second law, but the Newton-Euler equations of motion for rigid bodies. In addition, standard rigid-body dynamics also presumes that the joints connecting segments are ideal, providing well-defined reaction forces arising directly from the constraints on the motion. However, many biomechanical joints are not completely ideal in the sense that they allow for small motions between the bones, and these small motions are simultaneously difficult to observe and also depending on the forces in the system. This means that we cannot determine these motions before we know the forces and, as we just saw above, standard inverse dynamics requires us to know the motion before we can find the forces. So we are faced with a catch 22 problem: We cannot find the motion before we know the forces, and we cannot compute the forces without knowing the motions. This is where Force-Dependent Kinematics or FDK comes into the picture.
In this tutorial we are going to construct a very simple model of a knee to demonstrate what it is and how it works. The model is simple because it must be easy to understand and fast to build and analyse, but it shares its properties with much more complex body models that can really help us understand the detailed functions of real joints. This is what the model is going to be like:
This model is a knee extended by a single quadriceps muscle. The joint, however, is somewhat different from the idealized engineering joints you often see in musculoskeletal models. It comprises a circular condyle in contact with a flat tibial plateau. The contact is frictionless, so the condyle can in principle slide back and forth on the plateau. To stabilize the knee, two perpendicular springs are acting between the femur and tibia. The first spring is normal to the tibial plateau, and it represents the stiffness of the cartilage between the two parts. The second spring is parallel to the tibial plateau, and it represents the collective effect of the menisci and the ligaments.
Please go ahead and download a template of the model here, and then proceed to: