KNR 352
Quantitative Analysis in Biomechanics
Linear and Angular Kinematics During Landing
Use the landing video and data set on the web site. Refer to “Completing Calculations”
below for the equations necessary to perform the velocity and acceleration calculations.
By hand: OPTIONAL (submit pages of your calculations).
1. From 25 ms before ground contact until 25 ms after ground contact, calculate the
velocity of the HIP marker in the X and Y directions.
2. From 25 ms before ground contact up to and including the frame of ground
contact, calculate the acceleration of the HIP marker in the X and Y directions.
Use both Method 1 and Method 2, below, for the calculations.
a. Compare and contrast the acceleration values calculated using the two
methods.
3. Create the following graphs, using graph paper and coloured pens/pencils:
a.
Position, velocity and acceleration of the hip marker in the X direction.
b.
Position, velocity and acceleration of the hip marker in the Y direction.
Note: ensure that you align the position, velocity and acceleration data points
correctly over the appropriate time point.
c. Describe the kinematics of the hip marker in the X and the Y direction
(word processed). In your description, at least consider the known forces
acting on the marker in each direction and the time at which the force(s)
are applied to the body.
Using Excel: (print out a copy of your new file showing successful
calculations)
Linear Kinematics
4. Save the original data file onto your own disk. On a working copy of your saved
Excel file
a. Create new columns for X velocity, Y velocity, X acceleration and Y
acceleration
b. Into the appropriate column, program the equations listed below under
“Completing Calculations” to fill in the velocity and acceleration (separate
columns for each of the acceleration methods) data in each direction for
the hip marker.
c. Create, and print, Excel graphs of position, velocity and acceleration (both
methods) of the hip marker in both directions.
i. Describe the kinematics of the hip marker in the X and the Y
direction (word processed). In your description, at least consider
the known forces acting on the marker in each direction and the
time at which the force(s) are applied to the body.
Angular Kinematics (report all angles in degrees)
5. Using another working copy of your saved Excel file and the Excel operations:
a. Use the coordinates to generate a four-segment stick figure of the lander at
Touchdown (Frame 19).
i. Create by hand (use graph paper) OR using software.
b. Create new columns for Trunk, Thigh, Shank and Foot
i. Into each of the columns, program the equation to calculate the
segment angle using the X and Y coordinates of the appropriate
landmarks. All angles should be calculated from the Right
Horizontal.
c. Create new columns for Hip, Knee and Ankle
i. Into each of the columns, program the equation to calculate the
joint angle using the appropriate combination of segment angles. F
1. For the hip and knee joint, full extension should be 180
degrees, with flexion indicated by a decreasing joint angle.
2. For the ankle joint, the neutral position should be 90
degrees, with dorsiflexion < 90 degrees and plantarflexion
> 90 degrees.
d. Create, and print, using Excel (try to create one figure for part i and one
figure for part ii)
i. Position-time curves of the four segment angles
ii. Position-time curves of the three joint angles.
iii. Interpret the dorsiflexion at the ankle and flexion at the knee joint
by referring to the angles of the segments that meet to create the
joint. For example, as the knee flexes, explain whether the thigh or
the shank segment undergoes a greater change in angle. You may
want to create a position-time curve that shows both segments and
the joint angle (You may even want to use separate Y axes for the
segment and for the joint angle).
e. Compare the angles calculated in b and c to the stick figure created in a (at
Frame 19)
i. Do your calculated segment angles reflect the angles evident in the
stick figure?
1. If not, explain what is going on with the calculation, and
explain the necessary correction
ii. Do your calculated joint angles reflect the angles evident in the
stick figure?
a. If not, explain what is going on with the calculation,
and explain the necessary correction
6. Create new columns for the angular velocity of the hip, the knee and the ankle.
a. Calculate the angular velocity of the hip, knee and ankle joint using the
velocity equation below
b. For each of the hip, knee and ankle, create a single figure that presents the
angular position and angular velocity relative to time
i. You should use separate vertical axes for the position data and for
the velocity data to maintain resolution of the curves
c. Describe how well the critical points of the position and the velocity
curves match up.
Completing Calculations
(from Peak Motus 6.1 User Manual, page 61, Copyright 2001)
Calculating Velocity
Given a time series of position data, di, i = 1,…n, where d is the position data and “i” is
an instant in time, linear velocity is calculated discretely using the following algorithm,
where t is the time increment:
For “i” = 1, forward difference:
vi  (d i  2  4d i 1  3d i ) / 2t
For “i” = 2, …n –1, second order finite difference:
v i  (d i 1  d i 1 ) / 2t
For “i” = n, backward difference
vi  (d i 2  4d i 1  3d i ) / 2t
Calculating Acceleration:
Method 1: Acceleration can be calculated from the calculated velocity values, using the
same equations as above but substituting velocity for position.
Method 2: Acceleration can also be calculated directly from the position data, as follows:
Given a time series of position data, di, i = 1,…n, where d is the position data and “i” is
an instant in time, linear acceleration is calculated discretely suing the following
algorithm, where t is the time increment:
For “i” = 1, forward difference
ai  (2d i  5d i 1  4d i  2  d i 3 ) / t 2
for “i” = 2 and “i” = n-1, second order finite difference:
ai  (d i 1  2d i  d i 1 ) / t 2
for “i” = 3, …, n-2, fourth order central difference:
ai  0.0833(d i  2  16d i 1  30d i  16d i 1  d i  2 ) / t 2
for “i” = n, backward difference:
ai  (d i 3  4d i  2  5d i 1  2d i ) / t 2