Week 6 Kinematics

What is kinematics?

• The study of motion without regard. to its causes

  • Distance, speed, direction, rotation, pattern of motion

  • Kinematic quantities: time, position, displacement, velocity, acceleration (and rotational dialogues)

• Concerned with description and quantification

  • Not usually explanation of ‘why’

What are the patterns of motion in terms of rectilinear and curvilinear translation?

• Rectilinear Translation

  • All particles within the body move in a straight line at the same speed

• Curvilinear Translation

  • Particles within the body follow parallel paths, but motion is not linear

What is the difference between the rotational (angular) motion and general planar motion?

Rotational Motion:

• Particles in the object have rotated relative to some fixed axis

GPR:

• Any motion in a single plane, consisting of both translational and rotational motions

Why is kinematics important?

• Kinematics analyses of performance are invaluable for clinicians, physical education teachers and coaches

  • Learning motor skills involves gradual modification of movement kinematics

    • Reduction of kinematic variability

      • Learning to walk

  • Rehabilitation involves restoration of normal kinematics (joint or whole body)

• Kinematics spans both qualitative and quantitative forms of analysis.

What are benefits and drawbacks of qualitative kinematic analysis?

• Benefits

  • Does not require complex research equipment

  • Can be carried out quickly by coaches, educators, clinicians

• Drawbacks

  • Places ‘overload’ on the observer

  • Measurements difficult to compare - no outcome measures

  • Hypothesis testing and experimentation not possible

What are the benefits of quantitative kinematics analysis?

• Benefits

  • More objective answers; quantifiable data

  • Comparison with normative data or previous performance

• Drawbacks

  • Requires specialized equipment and expertise

What can be said about quantitative kinematic analysis?

• Kinematic variables serve as inputs for inverse dynamic analyses

  • Estimation of joint reaction forces and moments

How does distance differ from displacement?

• Distance: the length of the path travelled by the body

Displacement

• The straight line that connects the point’s position from one instant in time to another

  • Includes length (magnitude) and direction and, hence, is a vector quantity

  • As a vector quantity, displacements add according to the parallelogram law

How do we determine when we use distance versus displacement?

• Marathon Running?

• Amount of movement between2 points is small?

• Know initial and final positions of the object

• Displacement based measures are well suited for quantitative kinematic analyses using motion capture

What are displacement based measures?

• Video is a series of still images

  • We know the time interval between each image (ex. 1/thousandth of a second)

• We can calculate the displacement of a point in space between subsequent images

What is speed and velocity?

Speed: The rate of change of distance over time (m/s)

• Because distance is a scalar quantity, so is speed

• Travelling in a car

  • May have constant speed, but varying direction

• Average speed can give misleading conclusions

Velocity: the rate of change of position over time (where the change in position = displacement)

• using calculus, the derivative of displacement

What is an instantaneous velocity?

• Gives the veloctiy of an object at an instant in time

  • The 80 m mark in a 100m sprint

• If we sample the movement quickly enough (reduce time b/w subsequent images; reduce time between P and Q) the average velocity between adjacent images will be approximately equal to the instantaneous velocity

• For planar motion we need to account for x and y directions

• Velocity can be reported using either rectangular coordinates (x,y) or polar coordinates (r, theta)

• The same equations as average velocity but in this case angle of t is very small

  • Yes because velocity is a vector.

How does velocity differ on graphs?

• Constant velocity (Zero velocity)

• Constant velocity (non zero velocity)

  • rate of change of displacement (velocity) is uniform over time

• Non constant velocity (acceleration)

  • rate of change of displacement (velocity) is not uniform over time

What is acceleration?

• Rate of change of velocity

  • Rate of change of the rate of change of displacement

  • Second derivative of displacement

  • The first derivative of velocity

What should be noted on positive and negative accelerations?

• The direction (sign) of the acceleration vector depends on the direction (sign) of the velocity vector

  • Think of acceleration resulting from a force (F=ma)

  • The direction of acceleration is the same as the force (that would change the velocity of the object)

• AND negative acceleration does not always mean slowing down

How does direction affect acceleration?

• Since acceleration is a vector it has a direction, given by our cartesian coordinate system conventions

• The sign / polarity of acceleration depends on:

  • Whether the object is speeding up or slowing down

    • (MAGNITUDE)

  • Whether the object is moving in the + or - direction

    • (SENSE, in each of the x and y directions)

• The general principle for determining direction of acceleration:

  • If the object is speeding up, its acceleration is in the same direction as its velocity

  • If the object is slowing down, its acceleration is in the opposite direction as its velocity

What do kinematic equations do?

• Allow us to describe and represent the motion of object’s displacement, velocity, acceleration, time

• Allow us to determine unknown parameters

How could we calculate constant linear velocity?

• If there are no unbalanced forces, a body will continue to move along a straight line with constant velocity

  • We can determine the position of a body at any point in time, if we know its initial position, velocity and line of motion

  • Basically the equation for average velocity rearranged

  • Sf = si + Vit

What is constant linear acceleration?

• occurs whenever the resultant force acting on the body is non zero and constant

  • the position and velocity of the body at any instant can be predicted by knowing the initial position and initial valocity of the body

  • This equation is just the equation for avg. accel. rearranged

  • Final vel. = initial vel. + change in vel. due to accel. (and time of accel.)