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Difference between revisions of "Transverse Hinge Axis"
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*''Mandibular Opening of <math>0</math> <small><math display="inline">mm</math></small>:'' This parameter represents the centric recording model without wax interposed between the arches. With a mandibular opening of ''<math>0</math> <small><math display="inline">mm</math></small>'', the cuspal error is theoretically zero if the cusps were flat. However, if the cusps are inclined, the error may not be zero due to the inclination itself. *''Mandibular Opening of <math>3</math> <small><math display="inline">mm</math></small>:'' This parameter represents the centric recording model with wax interposed between the arches, generating a mandibular opening of ''<math>3</math> <small><math display="inline">mm</math></small>''. In this condition, even a small error in the localization of <math>_tHA</math> can cause a significant cuspal error, exacerbated by the inclination of the dental cusps. | *''Mandibular Opening of <math>0</math> <small><math display="inline">mm</math></small>:'' This parameter represents the centric recording model without wax interposed between the arches. With a mandibular opening of ''<math>0</math> <small><math display="inline">mm</math></small>'', the cuspal error is theoretically zero if the cusps were flat. However, if the cusps are inclined, the error may not be zero due to the inclination itself. *''Mandibular Opening of <math>3</math> <small><math display="inline">mm</math></small>:'' This parameter represents the centric recording model with wax interposed between the arches, generating a mandibular opening of ''<math>3</math> <small><math display="inline">mm</math></small>''. In this condition, even a small error in the localization of <math>_tHA</math> can cause a significant cuspal error, exacerbated by the inclination of the dental cusps. | ||
'''Simulation Results''' | |||
To address this problem, we use mathematical models and computer simulations to calculate how an error in the localization of <math>_tHA</math> translates into errors in the final positions of the dental cusps. We use various magnitudes of <math>_tHA</math> localization error (up to ''<math>10</math> <small><math display="inline">mm</math></small>'') and analyze the effect of these discrepancies both with centric recordings without wax and with the mouth closed (''<math>0</math> <small><math display="inline">mm</math></small>'') as well as with a slight mouth opening (''<math>3</math> <small><math display="inline">mm</math></small>''). In addition, we consider the inclination of the dental cusps, simulating errors on inclined cusps of ''<math>0^\circ</math>'' and ''<math>5^\circ</math>'' to make the model more realistic and applicable to actual clinical conditions. This approach allows us to better understand how localization errors affect the final result and provides valuable insights for improving precision in dental practices. | |||
In essence, with an opening of ''<math>0</math> <small><math display="inline">mm</math></small>'' in centric recordings without wax and non-inclined cusps (''<math>0^\circ</math>''), and with a <math>_tHA</math> error of ''<math>10</math> <small><math display="inline">mm</math></small>'' (10 steps from ''<math>0</math> <small><math display="inline">mm</math></small>'' to ''<math>10</math> <small><math display="inline">mm</math></small>''), the cuspal error is ''<math>0</math> <small><math display="inline">mm</math></small>''. With a mandibular opening of '''''<math>3</math> <small><math display="inline">mm</math></small>''''' and flat dental cusps (''<math>0^\circ</math>''), the cuspal error ranges from <math>0</math> ''<small><math display="inline">mm</math></small>'' in a situation of exact <math>_tHA</math> localization to <math>1</math> ''<small><math display="inline">mm</math></small>'' with a localization error of <math>10</math> ''<small><math display="inline">mm</math></small>''. However, even if we were to perform a centric recording without wax with a mandibular opening of ''<math>0</math> <small><math display="inline">mm</math></small>'', with dental cusps inclined by just ''<math>5^\circ</math>'', this condition introduces a vertical cuspal error due to the projection of the <math>_tHA</math> localization error along the inclination of the cusps. In this case, the error ranges from ''<math>0</math> <small><math display="inline">mm</math></small>'' in an exact localization of <math>_tHA</math> to <math>0.87</math> ''<small><math display="inline">mm</math></small>'' with a localization error of <math>10</math> ''<small><math display="inline">mm</math></small>''. | |||
====Script Pyhton: Errore Cuspidale con Apertura a 0 mm e Cuspidi Piatte'==== | ====Script Pyhton: Errore Cuspidale con Apertura a 0 mm e Cuspidi Piatte'==== | ||
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<syntaxhighlight lang="python"> | <syntaxhighlight lang="python"> | ||