{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Frame of reference\n", "\n", "\n", "> Marcos Duarte, Renato Naville Watanabe \n", "> [Laboratory of Biomechanics and Motor Control](http://pesquisa.ufabc.edu.br/bmclab) \n", "> Federal University of ABC, Brazil" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "Motion (a change of position in space with respect to time) is not an absolute concept; a reference is needed to describe the motion of the object in relation to this reference. Likewise, the state of such reference cannot be absolute in space and so motion is relative. \n", "A [frame of reference](http://en.wikipedia.org/wiki/Frame_of_reference) is the place with respect to we choose to describe the motion of an object. In this reference frame, we define a [coordinate system](http://en.wikipedia.org/wiki/Coordinate_system) (a set of axes) within which we measure the motion of an object (but frame of reference and coordinate system are often used interchangeably). \n", "\n", "Often, the choice of reference frame and coordinate system is made by convenience. However, there is an important distinction between reference frames when we deal with the dynamics of motion, where we are interested to understand the forces related to the motion of the object. In dynamics, we refer to [inertial frame of reference](http://en.wikipedia.org/wiki/Inertial_frame_of_reference) (a.k.a., Galilean reference frame) when the Newton's laws of motion in their simple form are valid in this frame and to non-inertial frame of reference when the Newton's laws in their simple form are not valid (in such reference frame, fictitious accelerations/forces appear). An inertial reference frame is at rest or moves at constant speed (because there is no absolute rest!), whereas a non-inertial reference frame is under acceleration (with respect to an inertial reference frame).\n", "\n", "The concept of frame of reference has changed drastically since Aristotle, Galileo, Newton, and Einstein. To read more about that and its philosophical implications, see [Space and Time: Inertial Frames](http://plato.stanford.edu/entries/spacetime-iframes/)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Frame of reference for human motion analysis\n", "\n", "In anatomy, we use a simplified reference frame composed by perpendicular planes to provide a standard reference for qualitatively describing the structures and movements of the human body, as shown in the next figure.\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Cartesian coordinate system\n", "\n", "As we perceive the surrounding space as three-dimensional, a convenient coordinate system is the [Cartesian coordinate system](http://en.wikipedia.org/wiki/Cartesian_coordinate_system) in the [Euclidean space](http://en.wikipedia.org/wiki/Euclidean_space) with three orthogonal axes as shown below. The axes directions are commonly defined by the [right-hand rule](http://en.wikipedia.org/wiki/Right-hand_rule) and attributed the letters X, Y, Z. The orthogonality of the Cartesian coordinate system is convenient for its use in classical mechanics, most of the times the structure of space is assumed having the [Euclidean geometry](http://en.wikipedia.org/wiki/Euclidean_geometry) and as consequence, the motion in different directions are independent of each other. \n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Standardizations in movement analysis\n", "\n", "The concept of reference frame in Biomechanics and motor control is very important and central to the understanding of human motion. For example, do we see, plan and control the movement of our hand with respect to reference frames within our body or in the environment we move? Or a combination of both? \n", "The figure below, although derived for a robotic system, illustrates well the concept that we might have to deal with multiple coordinate systems. \n", "\n", "\n", "\n", "For three-dimensional motion analysis in Biomechanics, we may use several different references frames for convenience and refer to them as global, laboratory, local, anatomical, or technical reference frames or coordinate systems (we will study this later). \n", "There has been proposed different standardizations on how to define frame of references for the main segments and joints of the human body. For instance, the International Society of Biomechanics has a [page listing standardization proposals](https://isbweb.org/activities/standards) by its standardization committee and subcommittees:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2016-09-28T22:32:13.159670", "start_time": "2016-09-28T22:32:13.140658" }, "scrolled": false, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "