Center of Mass - notes for biomechanics with examples of formulas and definitions PDF

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notes for biomechanics with examples of formulas and definitions ...

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Center of Mass, Modeling, Stability & Balance November 25, 2019 Center of Mass:  All bodies contain a unique point where if suspended motionless that body will remain balanced o This point is known as the center of gravity (COG)  the COM is the point on a rigid body where the mass is considered to be concentrated o for a symmetrical object of homogeneous density, the COM is the geometric center of the object o when the mass is not symmetrical or homogeneous the COM shifts in the direction of grater mass  recall that if net force is applied directly to an object that the object COM will undergo a linear acceleration proportional to and in the direction of the applied force regardless of the force’s application point o thus, we use the COM to represent the body during linear motion analyses  for example, we use the COM of the body or body segment to determine its linear displacement, velocity and acceleration o this allow us to ignore the shape and structure of the body being studied  for a human the COM varies depending on o Morphology:  The branch of biology that deals with the form and structure of organisms without consideration of organisms o The location of body segments Determining the Center of Mass:  Since COM of rigid bodies, it’s the same as its COG or balance point, the COM can be determined by suspending the object from a string at 2 or more locations on the object o Each time the object is suspended it will balance itself o Draw plump line each time the object is in equilibrium o The not where the plum line intersects… that will be the COM  Since weight of object acts through COM, a static system of balanced torques can also be used to determine COM (Reaction bored method)

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Reaction bored method: there are 3 moments in static equilibrium

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Each moment acts about the axis of rotation at that person feet The distance to the person COM would therefore be the perpendicular distance from that axis point to the application of the person weight

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If you weigh the person before they get in the reaction board, the only thing you don’t know is the distance to their COM from their feet

Modeling:  The human body can be divided into a number of body segments i.e. the head, trunk, thigh, shank, foot, upper arm, forearm and hand o Dividing the body into segments allows us to use link-segment modeling the track forces through the body by monitoring the acceleration and COM location of each body segment… a process known as inverse dynamics o Each segment is assumed to be rigid o Each of these body segments has its own anthropometric parameters  Anthropometric parameters include: o Segment end points o Segment masses o Segment COM o Segment radius of gyration and/or mass moment of inertia  They are assumed to be similar in particular populations  Its important to use anthropometric parameters or models or populations that closely resemble the one you are studying o This helps maintain validity and reduce errors in your study o Most models based on male population but female body composition (body fat percentage and distributions) and morphology (height, girths etc.)  How it works o Determine distal and proximal coordinates (X, Y) of body segments o Use XY coordinates to determine the length of each segments in the X and Y axes (Z-axis too if performing 3D analysis) o Once you have segments lengths you can use the percentage of segment lengths in your model to determine  Distance from the proximal marker to the COM  The radius of gyration or moment of inertia about the segment COM

What’s the mass of the thigh?  First determine total body mass of subject o Assume subject mass was 70kg  Then determine the percentage of total body mass attributed to the body segment from an anthropometric model o From the anthropometric model in slide 19, the thigh comprises 10.27% of total body mass  Then multiply the total body mass by percentage of the total body mass (as a decimal value) to obtain the segment mass Mass of the thigh = Pthigh = (total body mass) (percentage of total body mass) = (70kg) (0.1027) Pthigh = 7.19kg *** P indicates mass

Determining the Center of Mass:  Segmental Method o Once you determine COM location and mass for each body segment using the methods outlined, you can determine the total body COM location o Note: total body COM location is a function of each individual segments COM location and the mass of the segment itself

Some segments are more massive than others and therefore have larger influence on the location of the total body COM o Consonantly the calculations of the COM for a combination of segments requires a weighted average A weighted average assigns a weight to each value in a dataset o For our purposes, the dataset values are the segment COMs and the weights are the masses of each segments Typically, the weightings are normalized to some total value (i.e. total body weight), so that each weighting represents that particular values proportional influence on the total 

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How do we weigh each segment? o Multiply each segment (X Y) COM coordinate by its mass Now how we get the total body COM from the weighted segment COMs? o Sum up all weighted segments (X Y) COMs and then divide but the sum of all the segment masses or total body mass)  This will provide the total body (X Y) COM coordinates

Movement Strategies that Involve COM:  Flop technique in high jump o Allows one to move over the bar while their COM passes underneath it  Technique don’t have to jump as high to clear the bar

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Increasing vertical jump reach o Raise arms overhead to maximize COM relative to ground surface prior to takeof o Once in the air, the COM must follow the trajectory determined at takeof o At the apex of flight, drop one arm  Other segments must rise upward to maintain the COM location relative to earth

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Hang time o Legs and/or arms are raised at the beginning of the jump o The legs and arms are then lowered throughout the jump to maintain the paralic trajectory of the COM o As a result, the head and trunk appear suspended giving the illusion of “hang time” Push up supported by the feet vs knee : o Using the knee as the axis of rotation  Reduces the horizontal distance from COM to axis and the amount of mass to be moved  This reduces the moment and therefore the upper body muscle force required  Reduces the vertical distance COM must be raised o the result is push feels easier Reduced variability in COM during gait: o Skilled runner show less variation of their COM  Energy expended goes towards moving the COM forward and not up and down o Children show a lot of COM variability while running

Stability and Balance:  Stability is the resistance to: o Linear and angular acceleration o Disruption of equilibrium (static or dynamic, linear or angular/rotational)  Balance is the ability to control equilibrium or maintain stability 

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Liner stability is concerned with: o Body’s resistance being moved in a linear direction o Having a body’s direction changed or motion stopped Greater the force needed to upset the linear equilibrium the more stable the body Rotational stability is concerned with: o Body’s resistance to being rotated about a fixed point (i.e. falling or tripping over) The greater torque needed to upset rotational equilibrium the more stable the body Factors that afect stability include; o Mass  The more massive an object is, the greater the force required to accelerate it and the more stable the object is  i.e. bigger football lineman are more stable (harder to move) than smaller lineman o Friction  the greater the amount of friction between an object and the surfaces it contains, the greater the forces required to initiate or maintain motion

i.e. racing skates are designed to minimize the friction between the skate blade and the ice o Base of Support:  Area enclosed by the outermost edges of the body in contact with a supporting surface  When the COM moves outside of the base of support a moment is created (due to the force of gravity) which will cause the object to rotate (i.e. tip over)  The closer the COM is to edge of the base of support the less force applied to push it over that boundary  Keeping the COM in the middle of the base of support will increase stability  The greater the vertical displacement of the Com from base of support the greater the moment that can be created with an applied force… a smaller force is required to tip the object over Because human have: o High COM o Small base of support There is tendency to rotate about ankle joint in both the anteroposterior and mediolateral directions o This is known as postural sway  Increased sway correlates to fall in elderly In some instances, it is desired that stability be minimized o i.e. race starts  lifting hands of ground suddenly mean that weight is well outside of base of support and body is unstable 

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