Alysis of Pin-Supported Aluminum Beam Using Engauge Digitizer

Objective:

Determine sources of error that are inherent to measurements taken with Engauge Digitizer.

Description:

A rotary cutting mat with a 23inx35in grid was bolted onto ply wood. The bolts were placed to prevent mat flexure from distorting the grid lines. The ply wood was then mounted to a pre-threaded steel base. The grid was photographed with 6 ft. between the gridded surface and the camera. The camera was aligned at the 0,0 mark on the gridded mat. The image was imported into Engauge Digitizer to determine what error would exist in measurements. The points that were defined in Engauge Digitizer are shown in Fig. 1.

Fig. 1: Measurement Grid with User Defined Points

Values were recorded along the lines shown in Fig. 2 to determine the extent of inaccuracies.

Fig. 2: Lines Used to Determine Error

Results:

The first source of error discovered was in point placement. At 6ft distance between the target and camera, the smallest observable increment in point location is .026. Fig. 3 demonstrates where this value is displayed.

Fig.3: Point Placement Increment

Another source of error is a mismatch between the reference grid generated within Engauge Digitizer and the grid that is observed in the images. This mismatch iscaused by visual perspective andcan be seen in Fig. 4.

Fig. 4: Comparison of Generated Grid and Photographically Observed Grid

Between the user-defined axis reference points the deviation of digitally measured values follows the trend shown in Fig. 5.

Fig. 5: Discrepancy of Measured Values Between Defined Points

The deviation of digitally measured values away from a defined point can be seen in Fig. 6.

Fig. 6: Discrepancy of Measured Values Away From Defined Point

Attempts to use obtain simple polynomial functions to map digitally measured values to the physical dimensions have proven unsuccessful.

Recommendations:

If accurate correction of photographic distortion is desired, more detailed care will be required to properly align the camera with the measurement grid. This could be aided using a laser such as those typically found in inexpensive keychain-type laser pointers. An apparatus could be created with computer aided design and/or computer aided manufacturing to mount the pointer to a typical camera tripod. Fig. 7 shows an example of such a mount that could be set between the camera and a typical tripod.

Fig. 7: Possible Alignment Assisting Apparatus

Such an apparatus would ensure that the laser itself is aligned with the viewing vector of the camera. The offset of the pointer lens from the camera lens could then be measured. This offset could then be used to accurately place the camera relative to the grid. The shape of the laser on the grid could then assist in reducing or eliminating angular eccentricity. With eccentricities minimized or eliminated, the image could be closely measured to determine rates of change (partial derivatives) to quantify perspective distortion. With photographs taken at multiple distances, one could solve for the rate of change due to distance from target. A program could be written that could correct for parallax distortion as well as perspective distortion. Input parameters would likely include alignment point on the physical grid, measured rates of change, distance from camera to target, and distance from target to measurement grid. An inexpensive rangefinder can be used to assist distance measurements. One such rangefinder with accuracy to within .25 in. can be purchased at

Relevant Files and Documents:

E:\Results and Reports, End of Summer\Distortions and Error in Engauge Digitizer\Distance Distortions with Grid.xlsx

E:\Results and Reports, End of Summer\Distortions and Error in Engauge Digitizer\SolidWorks Files

E:\Results And Reports, End Of Summer\Distortions And Error In Engauge Digitizer\Distortions And Error In Engauge Digitizer.Docx 1