Introduction

In the previous chapter, we analyzed the forces involved in athletic movements and human motion by lumping the mass of each body segment at its geometric center. In reality, the mass of a body is distributed more or less uniformly throughout the body rather than being concentrated at a few points. In this chapter, we will lift the assumption of lumped masses. The objects that are under consideration are the ones that behave as rigid under the application of external forces. The distance between any two points in a rigid body does not change with time as the body undergoes motion. Therefore, the angle between any two line segments in a rigid object, and hence the shape of the object, remains constant. In reality, even the stiffest materials like steel or bone undergo subtle shape changes in response to applied forces. However, the extent of deformation is typically small so that the distance between any two particles in the object is hardly affected by the external forces acting on the object.

What is the significance of rigid body analysis to human body dynamics? First, the human body can be reasonably well represented by an interconnected chain of rigid links in the analysis of upper and lower limb movement. Typically, movement is a result of rotations performed at joints between the body segments. Then, some modes of human motion such as diving can be considered as a series of rapid shape changes followed by longer durations of constant shape motion. Additionally, the analysis presented here provides an estimate of the errors involved in using lumped-mass analysis of human movement and motion.

This chapter is focused on planar motion. We call the motion of a body planar when all particles in the body move in parallel planes. Vertical jumping, push-ups, somersaults, and biceps curls are all examples of planar motion. Other movements such as running or long jumping are essentially three dimensional. However, even in these modes of motion, planar analysis is a reasonable first model to provide insights into the complex interaction between forces and movement.

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