An upper limb model proposal for multi-body optimisation: effects of anatomical constraints on the kinematics

The upper limb consists of the arm, forearm, wrist, and hand bones. The humerus is the single bone of the upper arm region. Proximally, it has a large, spherical, smooth head that articulates with the glenoid cavity of the scapula to form the glenohumeral or shoulder joint. The margin of the head is the anatomical neck, a residual epiphyseal plate. Laterally it extends to form bony projections called the greater tubercle and the lesser tubercle. Next to the tubercles is the surgical neck, a...

In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
For instance, imagine a point A on a rigid body engaged in circular motion. The translational velocity of this particular point can be calculated by taking the time derivatives of the displacement equation, which essentially measures the...

Imagine a solid object involved in a general planar movement, with its center of mass pinpointed at a spot labeled G. The object's kinetic energy relative to an arbitrary point A can be quantified for each of its particles - the ith particle in this case. This measurement is achieved through the employment of the relative velocity definition. The position vector, known as rA, extends from point A to the mass element i.

The ulna and radius are parallel bones of the antebrachium or the forearm. The ulna lies medially and consists of a bony tip called the olecranon process at its proximal end. This hook-like projection articulates with the olecranon fossa of the humerus and forms the "hinged" ulnohumeral part of the elbow joint. This joint facilitates forearm extension and flexion while preventing its hyperextension. Similarly, the coronoid process, another bony projection on the proximal/anterior side...

The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.
Using the kinematic equations,...

Virtual work is a powerful method used to solve problems involving several connected rigid bodies. When the system is in equilibrium, virtual work is zero. This allows the calculation of the resulting forces when a system undergoes a virtual displacement. When attempting to analyze such a system, first, use a free-body diagram, where an independent coordinate represents the configuration of the links, and mark its deflected position resulting from the positive virtual displacement.
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