1 EXS 587 – Advanced Biomechanics Fall 2007 Dr. Moran Laboratory Experience: 2D Planar Kinematics (Applications Using MS Excel) Date: September 11, 2007 Lab Purpose: This lab is intended to provide the students with experience working with 2D kinematic (positional) data within MS Excel. Basic operating knowledge of MS Excel/Temporal/Planar Kinematics is required. Upon completion of this experience you should understand: • How to program within Excel (relative vs absolute referencing) • Finite differentiation techniques for calculating velocity/acceleration from position data • The ability to calculate relative joint angles from 2D marker data. Instructions: Please follow the step-by-step instructions – if you have any issues, please raise your hand and I will be by to assist. Golf Ball Position Data (Computing Time Derivatives) I. Please go to the course web page and download the Lab #1 Data. On the golf ball worksheet, this is time-position data of a golf ball dropping. II. The objective is to first calculate and plot the velocity of the golf ball falling. a. In column C compute the velocity by using the FORWARD DIFFERENCE Starting in Cell C3: Type: = (B4-B3) / (A4-A3) What was the result? Why is it negative? b. Now copy and paste C3 through cells C4 through C51. What happens if you paste into cell C52? Is this value correct? c. In column D compute the velocity by using the BACKWARD DIFFERENCE Starting in Cell D4: Type: = (B4-B3) / (A4-A3) Why is this method called “BACKWARD”? d. Now copy and paste D4 through cells D4 through D52. Why didn’t we paste into C3?2 e. In column E compute the velocity by using the CENTRAL DIFFERENCE Starting in Cell E4: Type: = (B5-B3) / (A5-A3) *notice with this method we DO NOT use the position data for that frame! Copy and paste E4 through cells E5 through E51. In E3 copy/paste the value from C3 (Forward Difference) and in E52 copy/paste the value in D52 (Backward Difference). So to compute the golf ball’s velocity we used a combination of the Forward Difference (first frame), Central Difference (middle frames) and Backward Difference (last frame) Methods. f. For column F compute the acceleration using the combined method just used for the velocity term. What is the value computed for cells E5 – E50? Does this value make sense in terms of the forces acting on the golf ball? What does it say about the rate of change of velocity? Why do the first 2 frames and last 2 frames have different acceleration terms? What could the researcher have done to avoid using the Forward and Backward Methods? (see page 21 in text) g. Make one graph with Position vs Time, Velocity vs Time and Acceleration vs. Time. Print graph and turn in with lab.3 Running Kinematic 2D Data (Computing Joint Angles) This data is from: Bogert, A.J. van den, and J.J. de Koning, "On optimal filtering for inverse dynamics analysis," Proc. 9th CSB Congress, Burnaby, B.C., pp. 214-215, 1996. Reflective markers were placed on the hip (ASIS), knee (lateral epicondyle), ankle (lateral malleolus) and toe. 2D Planar Lower Extremity Model Our objective is to determine the knee flexion/extension angle and ankle plantarflexion/dorsiflexion angle during running. These 2D joint angles can be computed through basic trigonometry or from simple vector mathematics. I. First you will need to compute the length of the thigh, shank, and foot segment. In order to do this you will need to create a vector for each segment and then find the length of this vector by utilizing the NORM. In cell D6 you will compute the THIGH SEGMENT LENGTH. Please compute by typing the following: =( (B12 – D12)^2 + (C12 – E12)^2 )^0.5 Using a similar approach compute the Shank and Foot segment length. THIGH SEGMENT LENGTH: _______________ SHANK SEGMENT LENGTH: ______________ FOOT SEGMENT LENGTH: _______________4 Give methodological reasons why these values would slightly change throughout the trial. Are these “real” changes to segment length? II. Next you will contact the Hip-Ankle distance for each FRAME of data. Please compute this distance (similar to Part I) for Frame #1 in cell J2 by typing: ( (B13-F13)^2 + (C13-G13)^2 ) ^0.5 Why do you need to compute this distance for each FRAME? III. Now you will compute the Knee Joint Angle. First you will compute the Knee Joint Angle by using the Law of Cosines. In cell K12 you will compute the Knee Joint Angle by for Frame #1 by typing: = 180 - DEGREES(ACOS ( ($D$6^2+$D$7^2-J12^2) / (2*$D$6*$D$7) ) ) You should get a value of 26.41 degrees. Now copy and paste the value of this cell in K13 – K5044. Notice how the formula changes throughout. What do the “$” signs in the formula signify? This is known as _____________ referencing in Excel. IV. You will compute the Knee Joint Angle by using the DOT PRODUCT. In cell L12 you will compute the Knee Joint Angle by for Frame #1 by typing: =180 - DEGREES(ACOS((((B12-D12)*(F12-D12))+(C12-E12)*(G12-E12))/($D$6*$D$7))) The values you get should equal the values you just computed using the Law of Cosines! Copy and paste the value in L12 throughout the entire column. Next make a plot of knee angle VS frame. Print this plot. Heel strike occurred at Frame 3001 – what was the knee angle (deg)? What was the peak knee flexion angle from the trial?5 V. OK now the hard(er) part. Compute the Ankle Angle in Column M. Print a plot of Ankle Angle vs. Frame. Refer to Figure 1.22 to get in the correct Medical joint angle system. VI. Typically in video analysis a marker may be blocked by another segment (ex: hip marker by the forearm/hand during arm swing). What can a researcher do if data for a marker that is missing for frames of