PTY1016 Biomechanics (Kinetics) PDF

PTY1016 Foundation of Physiotherapy 1: Movement Biomechanics Kinetics of Human Movement Seah Jianxing [email protected] Kinematics vs Kinetics of movements (e.g. gait) Kinem...

PTY1016 Foundation of Physiotherapy 1: Movement Biomechanics Kinetics of Human Movement Seah Jianxing [email protected] Kinematics vs Kinetics of movements (e.g. gait) Kinematics is the study of the geometry, pattern or form of motion with respect to time (not concerned with forces, but rather the details of the movement itself). Kinetics is the study of the forces associated with the motion. Knowledge of the patterns of the forces is necessary for an understanding https://www.tekscan.com/blog/medical/what-are-various-types- of the cause of any movement. gait-analysis Kinetic Concepts for Analyzing Human Motion Linear kinetics studies the causes of linear motion, while angular kinetics explains the causes of rotary motion. Basic Concepts Related to Kinetics Force is a push or a pull (product of mass and acceleration). Mass is the quantity of matter contained in an object. Inertia is the tendency of a body to maintain its current state of motion. Torque is the rotary effect of a force. Impulse is the product of the force and time over which the force acts. Linear Kinetics Newton’s Laws:Underlying Principles of Biomechanics Sir Isaac Newton (1687) Three Laws of Motion: 1. Inertia 2. Acceleration 3. Action-reaction Thi s Photo by Unknown Author i s licensed under CC BY Newton’s First Laws of Motion Law of Inertia: a body remains at rest or at a constant linear velocity except when compelled by an external force to change its state. Newton’s first law describes the case in which a body is in equilibrium (static or dynamic). Static equilibrium Dynamic equilibrium Newton’s Laws For example, a skater has a tendency to continue gliding with constant speed and direction because of inertia. Newton’s Second Laws of Motion Law of Acceleration: the acceleration of an object is directly proportionate to the amount of force applied and takes place in the direction in which the force is applied. Force is measured in newtons (N) Newton’s Third Laws of Motion Law of Action-Reaction: for every action, there is an equal and opposite reaction. When one body exerts a force on a second body, it exerts a reaction force that is equal in magnitude and opposite in direction of the first body. Law of Action-Reaction In accordance with the law of reaction, the weight of a box sitting on a table generates a reaction force by the table that is equal wt in magnitude and opposite in direction to the weight. R Law of Action-Reaction In accordance with Newton’s third law of motion, ground reaction forces are sustained with every footfall during walking/running. FV F FH Linear and angular (rotational) applications Angular ① ② ③ Neumann, D. A., (2017). Kinesiology of the musculoskeletal system : foundations for rehabilitation (Third edition.). Elsevier, chapter 4. Steps in constructing a free body diagram Step I: Identify and isolate the free body under consideration. Step II: Establish a coordinate reference frame. Step III: Draw the internal (muscular) and external forces that act on the system. Step IV: Draw the joint reaction force. Step V: Write the governing equations of motion. A frontal plane depiction of a free body diagram isolating the system as a right arm and ball combination: resultant shoulder abductor muscle force (M); glenohumeral joint reaction force (J); segment weight (S); and ball weight (B). The axis of rotation is shown as an open red circle at the glenohumeral joint. The X-Y coordinate reference frame is placed so the X axis is parallel with the upper extremity. Neumann, D. A., (2017). Kinesiology of the musculoskeletal system : foundations for rehabilitation (Third edition.). Elsevier, chapter 4. Mechanical Behavior of Bodies in Contact Linear momentum is defined as the vector quantity of motion that an object possesses (i.e., motion content of an object). The product of the mass and the velocity of an object. # Momentum = mv [units: kg m/s] where m is the mass, v is the velocity. Thi s Photo by Unknown Author i s licensed under CC BY Which Has More Momentum? Large object Mass=100 kg 10 X 100 momentum = > - = 1000kym/s Velocity= 10 m/s, east ↑ Small object Mass=10 kg Velocity= 100 m/s, east Conservation of momentum In the absence of external forces, the total momentum of a given system remains constant (does not change). * M1 = M2 (mv)1 = (mv)2 Newton's cradle Conservation of momentum and skaters same a h doftiness velocit Impulse Impulse (I) is a force applied to an object for a certain amount of time. It is calculated as the product of a force (F) and the time interval (t) over which the force acts. Impulse = F ∆ t [units: N ∙ s] (change final in force X The “follow-through” in sports Impulse-Momentum Relationship Relationship between impulse and momentum, derived from Newton’s second law: Force in Newton, N Momentum in kg ∙ m/s Impulse in N∙ s > - - - initial momentum find momentum Thus: Linear impulse = Change in linear momentum Impulse-Momentum Relationship Example: A man with a mass of 65 kg jumping from a squat position (at rest) into the air. Video analysis revealed that the velocity of his centre of mass at takeoff was 3.4 m/s. What is a) the impulse, and b) the force if it is applied over 0.2 s? a) Impulse Momentum = mass x velocity Impulse = change in momentum Therefore impulse is (65*3.4) – (65*0) = 221 N ∙ s b) Force Impulse = force * time Force = impulse / time = 221 / 0.2 = 1,105 N  Work, Power and Energy Work (in mechanical context) is defined as the product of the force (F) and displacement (d) in the direction of the force. * Work (W) = Force x displacement [units: Nm or Joules (J)] When the muscles of the human body produce tension resulting in the motion of a body segment, the muscles perform work on the body segment. Positive work Negative work Positive work – when the net force acting on a joint is in the same direction to the displacement. Negative work – when the net force acting on a joint is opposite in direction to the displacement. During isometric contraction, no mechanical work is done since there is no movement (although taking considerable effort). Work, Power and Energy Power is defined as the rate of doing work. ↓ Power (P) = Work / Change in time = W / ∆ t [units: Watts (W) or J (Joules)/s] or * face X velocity P = Fv Example: A 600 N man runs up a stairs of height of 8 m in 15 seconds. How much work is done, and how much power is generated? Solution: W = Fd = 600 x 8=4800 J P = W / t = 320 watts Work, Power and Energy Energy is defined as the capacity to do work (units is in Joules, J). Kinetic energy Potential energy Strain energy (or (energy resulting (gravitational): elastic energy; when from motion): object deforms): Strain energy Law of Conservation of Energy Energy cannot be created or destroyed; it is just transferred from one form to another. Maximum potential energy, minimum kinetic energy 6 W W https://cphysics.fandom.com/wiki/Kinetic_and_potential_energy Law of Conservation of Energy Example: Pole vaulter kinetic energy stored in the vaulter’s body during running. converted into strain energy in the pole when planting the pole in the box. strain energy in the pole is converted back into kinetic energy in the vertical direction of the vaulter’s body. at the peak height, kinetic energy of the body is converted to potential energy. just before landing on the mattress, PE → KE. upon landing on the mattress, KE is converted into impact energy dissipated through the mattress, sound waves and heat etc… Summary Linear kinetics is the study of the forces associated with linear motion. Ground reaction force (GRF) – the reaction force provided by the ground upon which one is moving. Linear momentum is the product of an object’s mass and its velocity. Total momentum in a given system remains constant barring the action of external forces. Changes in momentum result from impulses – external forces acting over a time interval. Mechanical work is the product of force and the displacement through which the force acts (positive or negative). Power is defined as the rate of doing work. Law of Conservation of Energy – Energy cannot be created or destroyed; it is just transferred from one form to another. Angular Kinetics Angular Kinetics * Angular kinetics is useful for the explanation of the causes of joint rotations. Newton’s laws have angular analogues that explains how torques create rotation. Newton’s Laws: Linear and Rotational Applications Torque (or Moment) The rotating effect of a force is called a torque, or moment of force. It is a vector quantity, calculated as the product of force (F) and moment arm (d). Nm Torque= Force  moment arm (distance) [units: Nm] Muscle Moment (or Joint Moment) Example: Net torque acting at the shoulder a ne Intendtorgebe one provided Forces of the anterior deltoid and long head of the biceps in shoulder flexing. Torque of these muscles: (60 x 0.06 + 90 x 0.03) = +6.3 Nm. Torque of the arm: (-40 x 0.4) = –16 Nm. Net torque acting at the shoulder: +6.3 Nm –16 Nm = –9.7 Nm (assuming no other shoulder flexors or extensors active). Resulting in an extension torque where the shoulder flexors are acting eccentrically to lower the arm.  Moment of Inertia Moment of inertia (I) is the inertial property of rotating bodies, which represents the resistance to angular acceleration based on both mass and the distance; the mass is distributed from the axis of rotation. [ Bending the joints of the upper and lower extremities brings segmental masses close to an axis of rotation which can decrease the limb’s moment of inertia. moment of ↓ distancefo. inertia Weight ring ↑ moment of invertic [ X moment of easier to ↓ invertic swing L 7 Although both bats have the same mass, bat A is harder to swing than bat B because the weight ring on it is positioned farther from the axis of rotation. Radius of Gyration (k) The radius of gyration (k) is radial distance from the axis of rotation to a point where the body's mass could be concentrated without altering its rotational characteristics - k changes as the axis of rotation changes axis of rotation ↑ Knee angle affects the radius of gyration (k2: lower leg and k3: foot)  Angular Momentum Angular momentum is defined as the quantity of angular motion that an object possesses. Angular momentum: L = I   [units: kg m2/s] where I = moment of inertia,  = angular velocity * Conservation of angular momentum: The total angular momentum of a given system remains constant in the absence of external forces. Moment Arm A moment is the result of force acting at a distance from the point of motion, or the axis. In mathematical terms, a moment (M) is the product of this distance (d) and the force (F): M = d × F In translational forces, d is the length of the lever arm (or the perpendicular distance from the force vector to the centre of motion), but in rotary forces, the lever arm is the moment arm (or the perpendicular distance from the force vector to the joint’s axis of motion). - Houglum, P. A., & Bertoti, D. B. (2012). Brunnstrom's Clinical Kinesiology. (6th ed.). Philadelphia: F. A. Davis Company. Torque Torque is force which is applied around an axis, producing joint motion. Torque (τ), or moment (when force is applied around an axis), is the product of a force times the perpendicular distance (d) from its line of action to the axis of motion (or its potential motion if the object is currently stationary): τ=F·d So d is the moment arm  same Forces and Torques (collinear forces) plane Vector composition of collinear forces. (A) Two force vectors are acting on the knee: the weight of the shank-and-foot segment (S) and the exercise weight (W) applied at the ankle. These forces are added to determine the resultant force (R). The X-Y coordinate frame indicates +Y as upward; the negative sign assigned to the forces indicates a downward pull. (B) The weight of the head (H) and the traction force (T) act along the same line but in opposite directions. R is the algebraic sum of these vectors. Neumann, D. A., (2017). Kinesiology of the musculoskeletal system : foundations for rehabilitation (Third edition.). Elsevier, chapter 4.  diff. plane Forces and Torques (coplanar forces) (A) Three forces are shown acting on a pelvis that is involved in single-limb standing over a right prosthetic hip joint. The forces are hip abductor muscle force (M), body weight (W), and prosthetic hip joint reaction force (J). (B) The polygon (or tip-to-tail) method is used to determine the magnitude and direction of the resultant force (R), based on the magnitude and direction of M and W. J in (A) is equal in magnitude and opposite in direction to R in (B). Determine the resultant force by polygon method L Neumann, D. A., (2017). Kinesiology of the musculoskeletal system : foundations for rehabilitation (Third edition.). Elsevier, chapter 4.  much not tested Forces and Torques (coplanar forces) Determine the resultant force by parallelogram method Parallelogram method is used to illustrate the effect of two force vectors ( F 1 and F 2 ) produced by contraction of the flexor digitorum superficialis and profundus muscles across the metacarpophalangeal (MCP) joint. The resultant force (R) vector creates a bowstringing force resisted by the flexor pulley and collateral ligaments (force P in blue) at the MCP joint. Neumann, D. A., (2017). Kinesiology of the musculoskeletal system : foundations for rehabilitation (Third edition.). Elsevier, chapter 4. Composing force vectors Collinear force vectors can be combined by simple addition or subtraction. Nonparallel, coplanar force vectors can be composed by using the polygon (tip-to-tail) method or the parallelogram method. Neumann, D. A., (2017). Kinesiology of the musculoskeletal system : foundations for rehabilitation (Third edition.). Elsevier, chapter 4.  tested * Resolution of Forces O O The muscle force (M) produced by the brachioradialis is represented as the hypotenuse (diagonal) of the rectangle. The X component (M X ) and the Y component (M Y ) are also indicated. The internal moment arm (IMA) is the perpendicular distance between the axis of rotation (red circle) and M Y. The X-Y coordinate reference frame is placed so the X axis is parallel with the body segment of interest; the thin black arrowheads point toward positive directions. Neumann, D. A., (2017). Kinesiology of the musculoskeletal system : foundations for rehabilitation (Third edition.). Elsevier, chapter 4. Internal vs External Forces acting on the body w S ext. = , torque g int torque = M O Resolution of internal forces (red) and external forces (black and green) for an individual performing an isometric knee extension exercise. (A) The following resultant force vectors are depicted: muscle force (M) of the knee extensors; shank-and-foot segment weight (S); and exercise weight (W) applied at the ankle. (B) The free body diagram shows the forces resolved into their X and Y components. The joint reaction force (J) is also shown (blue). In both panels A and B, the open circles mark the medial-lateral axis of rotation at the knee. (Vectors are not drawn to scale.) Observe that the X-Y coordinate reference frame is set so the X direction is parallel to the shank segment; thin black arrowheads point toward the positive direction. Neumann, D. A., (2017). Kinesiology of the musculoskeletal system : foundations for rehabilitation (Third edition.). Elsevier, chapter 4. ① Effect of change of joint angle on torque A Changing the angle of the elbow joint alters the angle-of-insertion of the muscle to the forearm. These changes, in turn, alter the magnitude of the X (M X ) and Y (M Y ) components of the biceps muscle force (M). Using trigonometric functions, the magnitudes of M X and M Y can be found for each position: (A) angle-of- a insertion of 20 degrees; (B) angle-of-insertion of 90 degrees; (C) angle-of-insertion of 45 degrees; and (D) angle-of-insertion of 15 ( degrees. Although the magnitude of M is assumed to be constant (120 N), the changing magnitude of M Y alters the internal torque joint'saxson significantly throughout the range of motion. The internal moment arm (IMA) is drawn as a brown line extending from the axis of rotation (black dot) to the point of application of M and remains constant throughout panels A to D. Note that the X-Y coordinate reference frame is set so the X direction is always parallel to the forearm segment; thin black arrowheads point toward the positive direction. Neumann, D. A., (2017). Kinesiology of the musculoskeletal system : foundations for rehabilitation (Third edition.). Elsevier, chapter 4.  L S Changing the angle of elbow flexion can alter both internal and external torque potential. (A) The 90-degree position of the elbow maximizes the potential for both the internal and the external torque. (B) With the forearm horizontal and the elbow closer to extension, the external torque remains maximal but the overall biceps force (M) must increase substantially to yield sufficient M Y force to support the weight. EMA, external moment arm; IMA, internal moment arm; M, muscle force; M Y , Y component of the muscle force; W, exercise weight. Neumann, D. A., (2017). Kinesiology of the musculoskeletal system : foundations for rehabilitation (Third edition.). Elsevier, chapter 4. Neumann, D. A., (2017). Kinesiology of the musculoskeletal system : foundations for rehabilitation (Third edition.). Elsevier, chapter 4. Neumann, D. A., (2017). Kinesiology of the musculoskeletal system : foundations for rehabilitation (Third edition.). Elsevier, chapter 4. Which position to produces the greatest B biggestdistancea of motion torque at the shoulder? Houglum, P. A., & Bertoti, D. B. (2012). Brunnstrom's Clinical Kinesiology. (6th ed.). Philadelphia: F. A. Davis Company.  < > - dida easier to lift :. Blift using Using proper body mechanics includes moving objects close to the body. In (A), the object has a long lever arm and will place a much greater force on the body than the object in (B) when it is brought closer to the body so its lever arm is shortened. Houglum, P. A., & Bertoti, D. B. (2012). Brunnstrom's Clinical Kinesiology. (6th ed.). Philadelphia: F. A. Davis Company. Resolution of forces Figure 2.16 Two forces acting in different directions from the same point create a resultant vector. The resultant vector is made up of a rotation force and a force that either compresses or distracts the joint. A) Shows a large compression force vector and small rotational force vector. B) Shows rotational and distraction forces that are close to equal to each other but create a larger resultant force than either of them. C) Since the applied force vector is perpendicular to the lever, there is no distraction or compression force, so all of the muscle’s force rotates the segment Houglum, P. A., & Bertoti, D. B. (2012). Brunnstrom's Clinical Kinesiology. (6th ed.). Philadelphia: F. A. Davis Company. By resolving the forces generated by clavicular and sternal portions of the pectoralis major muscle (CPM and SPM respectively), what shoulder motion results? Houglum, P. A., & Bertoti, D. B. (2012). Brunnstrom's Clinical Kinesiology. (6th ed.). Philadelphia: F. A. Davis Company.  WN CON M = S B A Based on these two drawings of the deltoid, in which anatomical position would a constant muscle contraction produce more force to elevate the arm? Why? B Has larger. MA. Houglum, P. A., & Bertoti, D. B. (2012). Brunnstrom's Clinical Kinesiology. (6th ed.). Philadelphia: F. A. Davis Company. Centre of gravity and centre of mass Centre of gravity (CG) of an object or body is the theoretical point around which the mass of the object is balanced and around which that gravity acts. Also called the centre of mass (COM) – COM is the point of origin for gravity’s vector force. The CG of the adult body in the anatomic position is slightly anterior to the second sacral vertebra (55% of a person’s height). It is usually near the level of ASIS. wide in F bone hip · ? Usually higher in male than female. Why? > - Ch lower in M mass Change of body position changes CG. UB move > - CG higher Consider sit-ups, why is it easier to perform with arms stretched out than hands behind the head? Houglum, P. A., & Bertoti, D. B. (2012). Brunnstrom's Clinical Kinesiology. (6th ed.). Philadelphia: F. A. Davis Company.  Where is the CG in each of the pictures? Base of support and balance A body is stable when the line of gravity runs through the center of its base of support. A body’s base of support (BOS) is the area within the points of contact of the less efficient body and any object the individual relies on for then normal - support. stance walking Houglum, P. A., & Bertoti, D. B. (2012). Brunnstrom's Clinical Kinesiology. (6th ed.). Philadelphia: F. A. Davis Company. · A TO A CAL for moment force 2 perpendicular. : x (M) distene (m). 3 mount arm resolution of forces