Modeling study of seated reach envelopes based on spherical harmonics with consideration of the difficulty ratings

Reach envelopes are very useful for the design and layout of controls. In building reach envelopes, one of the key problems is to represent the reach limits accurately and conveniently. Spherical harmonics are proved to be accurate and convenient method for fitting of the reach capability envelopes. However, extensive study are required on what components of spherical harmonics are needed in fitting the envelope surfaces. For applications in the vehicle industry, an inevitable issue is to construct reach limit surfaces with consideration of the seating positions of the drivers, and it is desirable to use population envelopes rather than individual envelopes. However, it is relatively inconvenient to acquire reach envelopes via a test considering the seating positions of the drivers. In addition, the acquired envelopes are usually unsuitable for use with other vehicle models because they are dependent on the current cab packaging parameters. Therefore, it is of great significance to construct reach envelopes for real vehicle conditions based on individual capability data considering seating positions. Moreover, traditional reach envelopes provide little information regarding the assessment of reach difficulty. The application of reach envelopes will improve design quality by providing difficulty-rating information about reach operations. In this paper, using the laboratory data of seated reach with consideration of the subjective difficulty ratings, the method of modeling reach envelopes is studied based on spherical harmonics. The surface fitting using spherical harmonics is conducted for circumstances both with and without seat adjustments. For use with adjustable seat, the seating position model is introduced to re-locate the test data. The surface fitting is conducted for both population and individual reach envelopes, as well as for boundary envelopes. Comparison of the envelopes of adjustable seat and the SAE J287 control reach envelope shows that the latter is nearly at the middle difficulty level. It is also found that the abilities of reach envelope models in expressing the shape of the reach limits based on spherical harmonics depends both on the terms in the model expression and on the data used to fit the envelope surfaces.