# BIOMECHANICS 20172018 Linear Angular Kinematics LINEAR KINEMATICS Do

BIOMECHANICS 20172018 Linear & Angular Kinematics

LINEAR KINEMATICS Do you still remember the meaning of kinematics? Are you familiar with these kinematics quantities? • Distance, Displacement – explain the difference. • Speed, Velocity • Acceleration Exercise 1 With a proper sketch, explain the difference between average and instantaneous velocity.

LINEAR KINEMATICS ACCELERATION AND DIRECTION OF MOTIONS -ve direction +ve direction Does positive acceleration indicate that you/subject are increasing your/their speed only? Does the polarity of acceleration is dependence/independence of motion direction? “In the middle of a 100 m sprint, a runner is running with a constant, maximum velocity”. What is his acceleration at this point of time?

Remember this? ? ? How do you terms the movement of this person in the air? What are the forces acting on his/her body?

LINEAR KINEMATICS “PROJECTILE MOTION” 1. Main concept prior to mathematical equations. When projectile travel through air, only air resistance and gravity act on it. If the air resistance is to be neglected, only gravitational acceleration act on the projectile. Gravitational acceleration is constant, and thus, the projectile undergoes constant acceleration. Therefore, we need to understand the constant acceleration related equations. 2. What are the parameters influencing projectile motion?

LINEAR KINEMATICS “PROJECTILE MOTION” Gravitational acceleration is constant, and thus, the projectile undergoes constant acceleration. Therefore, we need to understand the constant acceleration related equations. a = aconstant = dv/dt

LINEAR KINEMATICS “PROJECTILE MOTION” Factors Influencing Projectile Trajectory (Flight Path) • What are the factors? • Which part of the trajectory being influenced? • Trajectory shape • Trajectory size or length • Flight time and horizontal distance • The object involve in projectile motion is considered as a particle or rigid body? • Does airplane with functional engine qualify to be considered as projectile when travel through air?

LINEAR KINEMATICS “PROJECTILE MOTION” Influence of projection angle on projectile trajectory ᶱ

LINEAR KINEMATICS “PROJECTILE MOTION” Influence of projection angle on projectile trajectory 90° 0° <x< 90° -90° <x< 0° What you could infer about the shape of the trajectory with respect to the changes in projection angle (similar speed). Could we used the term “similar velocity”?

LINEAR KINEMATICS “PROJECTILE MOTION” Influence of projection angle on projectile trajectory The Effect of Projection Angle on Range (Relative Projection Height = 0) Projection Speed (m/s) 10 10 10 Projection Angle (degrees) 10 20 30 40 45 50 60 70 80 Range (m) 3. 49 6. 55 8. 83 10. 04 10. 19 10. 04 8. 83 6. 55 3. 49 What could you infer from this table about the influence of projection angle on range or length or size of the projectile trajectory?

LINEAR KINEMATICS “PROJECTILE MOTION” Influence of projection speed on projectile trajectory When other parameters are constant, projection speed determines the length or size of a projectile's trajectory. Body projected at oblique angle (0° < Ɵ <90°), the speed determines the height and horizontal length of the trajectory.

LINEAR KINEMATICS “PROJECTILE MOTION” Influence of projection speed on projectile trajectory Variation in projection speed (constant projection angle)

LINEAR KINEMATICS “PROJECTILE MOTION” Influence of Relative Projection Height Projectile Trajectory The difference in the height from which the body is initially projected and the height at which it stops. The shape of the projectile trajectory influenced by the relative projection height.

LINEAR KINEMATICS “PROJECTILE MOTION” Optimum Conditions All the three factors (angle, speed and relative height) are interrelated. Any change in one results in a change of the others. There are relationships among projection speed, height and angle, such that when one is shifted closer to the optimal, another moves farther away from optimum. This is because human are not machines, and human anatomy dictates certain constraints. In shot put, release speed decreases with increasing release angle at 1. 7 (m/s) / rad, and decreases with increasing release height at 0. 8 (m/s) / m. In the shot put and the discus, researcher have found that optimal angle is athlete-specific, ranging from 35° to 44° among elite performers. In long jump, the actual take off angle employed by elite long jumpers range from approximately 18° to 27°, as compared to theoritically optimum angle of take off that is 45°.

1 st Exercise to be submitted by Today • Derive equation relating (i) Vfinal (m/s), Vinitial(m/s), t (s) and acceleration(m/s 2), (ii) Position (S), velocity (V), acceleration (m/s 2) and t(s). 2 nd half 1 st half (iii) The basketball is subjected to gravitational acceleration. You were asked to calculate the total travelling time from release to the final location. In determining the travelling time, how do you consider the polarity of gravitational acceleration in the following case: (a) travel upwards (from initial position to maximum height) (b) travel downwards (from maximum height to final position)

The polarity of gravitational acceleration depends on the direction of the vertical axis considered when drawing the FBD. If you plot the vertical axis to be downward (+ve), the g is always +ve. However, if you plot the vertical axis to be upwards (+ve), the g is always -ve. (iv) Should we use displacement or distance to solve problem related to projectile motion?

WALKING – EVENTS & PERIODS

RUNNING - EVENTS & PERIODS

Human Gait Analysis Linear Kinematics The stride is subdivided into steps. A STEP is a portion of the stride from an event (toe off of left leg) occuring on one leg to the same event (toe off of right leg) occuring on the opposite leg. 2 STEPS is equal to 1 STRIDE.

Human Gait Analysis Linear Kinematics - Walking A STRIDE is defined as the interval between an event of one foot (e. g. heel-strike) and the next occurrence of the same event of the same foot. STRIDE LENGTH is the distance between the position of one foot and the subsequent position of the same foot.

Human Gait Analysis Other Linear Kinematics Parameters in Gait Cadence (steps/min) – does not conform with SI (Systeme International), therefore, use Cycle Time (also known as Stride Time) Cycle time (s) = 120/cadence (steps/min) (If u walk with 120 steps/min, means your Cycle Time is 1 s for 1 stride) Stride Rate (Hz) Stance (% of gait cycle) Swing (% of gait cycle)

ANGULAR KINEMATICS

ANGULAR KINEMATICS Measuring Orientation of Object in 2 D (Measuring Angle)? +ve angles Angle is measured either counter clock wise or clock sise w. r. t horizontal line. -ve angles Rotation occurs about an axis that pass through origin of the coordinate system and perpendicular to this page. The SI unit is the radian…

ANGULAR KINEMATICS Measuring Angles Relative Angles (joint angles) The angle between the longitudinal axis of two adjacent segments. Absolute Angles (segment angles) The angle between a segment and the right horizontal of the distal end. Should be measured consistently on same side joint Should be consistently measured in the same direction from a single reference - either horizontal or vertical Straight fully extended position is generally defined as 0 degrees

ANGULAR KINEMATICS Segment Angles (Absolute Angles) qtrunk qthigh qleg qfoot RIGHT sagittal view segment angles/absolute angles

Calculating Absolute Angles • Absolute angles can be calculated from the endpoint coordinates by using the arctangent (inverse tangent) function. (x 2, y 2) opp = y 2 -y 1 adj = x 2 -x 1 (x 1, y 1) q adj opp

ANGULAR KINEMATICS Absolute Angle What is the angle of shank (leg) segment w. r. t the right horizontal axis? Ɵthigh

ANGULAR KINEMATICS Absolute Angle What is the angle of thigh segment w. r. t the right horizontal axis? Ɵthigh This is measured CW from left horizontal and need to be added with 180 degree. Answer is 105. 4 °

ANGULAR KINEMATICS Joint Angle between adjacent body segments. The concept is, in anatomy reference position, the relative angle is always zero.

ANGULAR KINEMATICS HIP Angle Hip angle > 0 degree, Hip flexion Hip angle < 0 degree, hip extension If = 0 degree, neutral position

ANGULAR KINEMATICS Knee Angle In HUMAN LOCOMOTION knee angle is always > 0. Knee angle progressive greater, it is flexing. Knee angle progressively smaller, it is extending. Negative knee angle, hyperextension of knee.

ANGULAR KINEMATICS Ankle Angle To make it oscillate about 0 degree, add 90 degree. Thus negative angle is dorsiflexion, positive angle is plantarflexion. Θfoot is measured from horizontal line passing through toe and head of 5 th metatarsal & line pass through and head of 5 th metatarsal and heel. Therefore, when the foot is dorsiflexing, the ankle angle is -ve.

ANGULAR KINEMATICS Ankle Angle Determine all kinematics parameters of trunk, Thigh, Leg and Foot. Let us do this exercise, Trx = -3. 95, Try = 523. 08 Thx = -210. 15, Thy = 317. 14 Lx = -113. 03, Ly = 377. 88 Fx = -181. 92, Fy = -67. 95

ANGULAR KINEMATICS Ankle Angle Take this case as example, Trx = -3. 95, Try = 523. 08 Thx = -210. 15, Thy = 317. 14 Lx = -113. 03, Ly = 377. 88 Fx = -181. 92, Fy = -67. 95 Dorsi flexion at ankle. +ve is plantar flex

ANGULAR KINEMATICS Rear Foot Angle Familiar with Subtalar Joint? The motion of subtalar joint in a 2 D analysis in considered to be in the frontal plane. The REAR FOOT ANGLE represents the motion of the subtalar joint.

ANGULAR KINEMATICS Calculating Rear Foot Angle Ɵrearfoot = Ɵleg - Ɵcalcaneus Ɵrearfoot Calcaneal Eversion Calcaneal Inversion

ANGULAR KINEMATICS Angular Velocity Generally presented as degree/second. ω=dθ/dt (rad/s) Angular Acceleration α=dω/dt (rad/s 2)

ANGULAR KINEMATICS - EXERCISE Figure 9 -18 shows the angular position, velocity and acceleration of thigh (absolute angle) during support phase. Could you explain the movement of thigh segment? Anglular position (deg) Anglular velocity (deg/s) Anglular acceleration (deg/s/s)

ANGULAR KINEMATICS Relationship Between Linear and Angular Motion Linear and angular displacement - s = rΘ (Θ is in radian) Linear and angular velocity - v = rω A case of increasing linear velocity of ball in soccer, what player do? Increase angular velocity of lower extremity segment Increase the length of the extremity In Golf, Different club length and club head loft. Linear and angular acceleration - a = d/dt(rω) = (rα)et + (vω)er = (rα)et + (v 2/r) er Tangential and Centripetal Acceleration (Radial Acceleration)

ANGULAR KINEMATICS IN WALKING The greatest range of motion occurs in the saggital plane and segment movement in this plane are often used to describe the gait characteristics.

ANGULAR KINEMATICS IN WALKING At initial touch down (Heel Strike), the hip flexion angle was reported to be in the range of 35 to 40 degrees (Black Solid Line - Biomechanical Basis of Human Movement) Initial touch down (Heel Strike), the knee is flexed and to be in the range of 10 to 15 degrees for walking. After touch down, the knee flexes to values ranging from 20 to 25 degrees in walking. The knee flexion movement lower the body in stance.

ANGULAR KINEMATICS IN WALKING After touch down (Heel Strike), the amount of hip flexion angle reduces over the course of support until toe off, at which 0 to 3 degrees of hip extension in walking. Vertical Solid Black Line indicates the border between stance and swing phase.

ANGULAR KINEMATICS IN WALKING When the limb is off the ground in the swing phase, hip flexion maximum values are reported in the range of 35 to 50 degrees for walking. Vertical Solid Black Line indicates the border between stance and swing phase.

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