! definition of moment and moment arm. ! conventions for defining moment direction. ! addition of moments, moments due to force

Transcription

1 oment and Toque Ozkaya and Nodin, Ch. 3 (p ) Outline! definition of moment and moment am! conventions fo defining moment diection! addition of moments, moments due to foce components! moments due to extenal foces! moments due to muscles! tanslation of foces and equivalent systems oments cause twisting o bending! effect of a foce on a igid body depends on whee it is applied! toque (T) o moment (): measue of the tendency of a foce to cause otation o bending about a specific axis! units of N m = mg oment is foce times distance! the moment that a foce poduces about a fixed point O is equal to the foce times the pependicula distance fom O to the line of action of the foce d O = v d! 2 d! = "moment am" d 1 ( O ) 2 > ( O ) 1 T O 1 = 100 N 2 = 100 N

2 oment am is pependicula to line of action of foce ake sue you calculate moment based on the moment am, not the distance fom the point of foce application to the axis of otation. P d d 3 3 oment is a Vecto! a moment has both magnitude and diection! in static equilibium poblems, thee is no stict convention fo defining positive and negative moments! we will usually efe to a CCW moments as positive, and a CW moments as negative! moments can be epesented in diagams one of two ways! the diection of O is Right Hand Rule! pependicula to the plane fomed by and O! detemined by the ight hand ule! ight hand ule: identify the diection that the moment tends to cause the body to otate about point O! oient you ight hand so this diection is illustated by the act of culing you finges into inceased flexion! you thumb will be pointing in the diection of the moment epesentation that shows the diection of O oment addition! oments about a given axis add algebaically! Be caeful to account fo the sign (i.e., diection) of each moment + O =!2 "W 2! 4 "W 1

3 oment calculations can be simplified by using foce components! It is often convenient to esolve a foce into its x, y, and z components in ode to calculate the moment it geneates at a specific location. + B = y (x A! x B )! x (y A! y B ) Extenal oces Ceate oments The effect of extenal loads on poducing human body movements, and geneating intenal foces and stesses, depends on the moments they ceate. Conside, fo example, how the angle! influencces the feasibility o effot involved in the bench pess execise. uscles Ceate oments The ability of muscles to stabilize the body unde extenal loads, and poduce human body movements, is due thei ability to ceate moments (o toques) about joints. If the line of action of a muscle foce passes though a joint axis of otation, it cannot stabilize o otate that joint. uscles have small moment ams Compaed to extenal loads, muscles have small moment ams with espect to joint they span. Advantage: given the limited defomation that muscles can undego, thei close poximity to joints allows fo lage anges of joint otation Disadvantage: high muscle foces (and theefoe joint foces) ae equied to balance extenal loads

4 Elbow angle effects moment am of elbow flexo muscles oment Am (mm) Bachialis Biceps Bachioadialis oces can be moved by eplacing them with a foce and a moment A foce applied to a igid body at a location A can be tanslated to anothe location O on the body, if a moment (o couple) O is also added at O. The location of O will affect the magnitude of O. 2D Elbow Angle (degees) 3D ultiple foces can be eplaced with a foce and a moment ultiple foces applied to a igid body can be eplaced by a single esultant foce and a single moment, acting at any location on the body. The location will affect the esultant moment, but not the esultant foce. ultiple extenal loads Equivalent esultant load and moment Equivalent single load Review Questions! How is a moment defined (mathematically)?! How is a moment am defined?! How is the ight hand ule used to detemine the diection of a moment?! How do moments add?! How can seveal foces be eplaced with a single moment and foce?! How does elbow otation affect the moment am of elbow flexo muscles? Does this explain why elbow stength vaies with elbow angle?

5 Tutoial poblems: 1. Detemine the magnitude of x, y, and z at the oigin O, in tems of foce components x, y, and z, and distances x A, y A, and z A. 2. Detemine moments at the elbow (point B) and shoulde (point A) due to the vetical load.