Masticationpedia

Store:Asse Cerniera Verticale parte 2

Store Discussion
Revision as of 13:41, 2 February 2025 by Gianni (talk | contribs)
Go to top

Rappresentazione spazio temporale dei markers da rivedere

Condilo Laterotrusivo

Questo paragrafo descrive il calcolo delle distanze e degli angoli tra segmenti in un piano 2D, applicati alla cinematica mandibolare. In particolare, si analizzano i movimenti articolari dei condili durante il ciclo masticatorio, rappresentati nella Figura 5 e nella Tabella 1.

Tabella 1
Tracciato masticatorio Markers Distanza (mm) Direzione Direzione Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Y}
Figura 2: Marker dei punti nel ciclo masticatorio
Figura 5: Marker sovrapposti in Geogebra sul tracciato del condilo laterotrusivo 		2 1.734 Protrusiva Parallela
3 4.99 Protrusiva Lateralizzazione
4 6.59 Protrusiva Lateralizzazione
5 3.66 Inversione Inversione
6 0.923 Retrusiva Lateralizzazione
7* 0.898 Protrusiva Medializzazione
8 0.257 Protrusiva Medializzazione

Dalla figura e dalla tabella emerge che il punto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7L_c} rappresenta l'inversione del moto condilare, con il passaggio verso un percorso mediale diretto alla massima intercuspidazione. La distanza tra il punto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7L_c} e Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1L_c} , pari a circa Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0.898 \, \text{mm}} , definisce il movimento di Bennett.

La direzione angolare è stata calcolata come: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta = 131.87^\circ} e Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta' = 42^\circ} .

Per approfondire, il calcolo dettagliato è riportato di seguito:  Info.pngCalcolo dettagliato: distanza tra Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_1 = (58.3, -50.9)} e Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_7 = (44, -34.9)} , distanza euclidea Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{(-14.3)^2 + (16)^2} \approx 21.47 \, \text{pixel}} , convertita in mm come Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 21.47 \times 0.04184 \approx 0.898 \, \text{mm}} , angolo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta = \arccos(-0.6665) \approx 131.87^\circ} .

Molare Laterotrusivo

Questo paragrafo analizza i movimenti articolari del molare ipsilaterale al condilo laterotrusivo, basandosi sul calcolo delle distanze tra punti e degli angoli tra vettori mediante trigonometria vettoriale (Figura 6 e Tabella 2).

Tabella 2
Tracciato masticatorio Markers Distanza (mm) Direzione Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X} Direzione dinamica Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Y}
Figura 3: Distanze e direzioni del molare ipsilaterale alla laterotrusione
Figura 6: Marker grafici rilevati dal 'Replicator' durante la masticazione sul lato destro 		2 0.39 Indietro Lateralizzazione
3 2.18 Indietro Lateralizzazione
4 3.57 Indietro Lateralizzazione
5 5.68 Indietro Lateralizzazione
6 6.76 Indietro Inversione
7* 3.93 Indietro Medializzazione
8 1.15 Indietro Medializzazione

Osservando la figura e la tabella, si evidenziano le distanze e le direzioni dei punti marcati. In particolare, la distanza tra il punto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7L_m} e il punto iniziale Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1L_m} è stata calcolata come circa Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3.93 \,_\text{mm}} , con un angolo tra i vettori pari a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 73^\circ} . Info.pngCalcolo dettagliato: 1. Definizione dei vettori: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{AB} = 7L_m - 1L_m = (255.7, -816.0) - (345.2, -844.5) = (-89.5, 28.5)} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{AC} = R_p - 1L_m = (346.6, -727.1) - (345.2, -844.5) = (1.4, 117.4)} 2. Magnitudine dei vettori: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |\vec{AB}| = \sqrt{(-89.5)^2 + (28.5)^2} \approx 93.93} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |\vec{AC}| = \sqrt{(1.4)^2 + (117.4)^2} \approx 117.41} 3. Prodotto scalare: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{AB} \cdot \vec{AC} = (-89.5)(1.4) + (28.5)(117.4) = 2928.4} 4. Calcolo dell'angolo: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cos(\theta) = \frac{\vec{AB} \cdot \vec{AC}}{|\vec{AB}| \cdot |\vec{AC}|} = \frac{2928.4}{93.93 \cdot 117.41} \approx 0.292} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta = \arccos(0.292) \approx 73.02^\circ}

Area Incisale

Questo paragrafo analizza i movimenti articolari dell’incisivo sul lato lavorante. Utilizzando le coordinate dei punti Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1_I} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7_I} e Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_p^+} in uno spazio 2D, sono calcolate le distanze lineari e l’angolo tra i segmenti che collegano questi punti.(Figura 7, tabella 3)

Tabella 3
Tracciato masticatorio Markers Distanza (mm) Direzione Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X} Direzione dinamica Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Y}
Figura 3: Distanze tra punti dell'incisivo
Figura 7: Markers grafici rilevati dal 'Replicator' durante la masticazione nell'area incisale sul lato destro. 		2 0.69 Retrusiva Lateralizzazione
3 2.30 Retrusiva Lateralizzazione
4 4.61 Retrusiva Lateralizzazione
5 7.58 Protrusiva Lateralizzazione
6 8.54 Retrusiva Inversione
7* 5.12 Retrusiva Medializzazione
8 1.75 Retrusiva Medializzazione

Per i tracciati dell’area incisale, la distanza tra i punti Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1_I} e Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7_I} è di Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5.12 \, \text{mm}} , con un angolo calcolato approssimativamente pari a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 85.1^\circ} .

Per approfondire i calcoli, ecco la spiegazione dettagliata Info.pngCalcolo dettagliato: Coordinate dei punti: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1_I = (631.5, -1151.8)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7_I = (509.6, -1139.9)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_p^+ = (634.3, -912.8)} . Vettori: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{1I7I} = (-121.9, 11.9)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{1IR_p^+} = (2.8, 239)} . Norme: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |\vec{1I7I}| = \sqrt{(-121.9)^2 + (11.9)^2} \approx 122.49} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |\vec{1IR_p^+}| = \sqrt{(2.8)^2 + (239)^2} \approx 238.95} . Prodotto scalare: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{1I7I} \cdot \vec{1IR_p^+} = (-121.9)(2.8) + (11.9)(239) \approx 2502.78} . Coseno dell’angolo: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cos(\theta) = \frac{\vec{1I7I} \cdot \vec{1IR_p^+}}{|\vec{1I7I}| \cdot |\vec{1IR_p^+}|} = \frac{2502.78}{122.49 \cdot 238.95} \approx 0.0855} . Angolo: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta = \arccos(0.0855) \approx 85.1^\circ} .

Molare mediotrusivo

L’analisi del moto cinematico mandibolare nel molare mediotrusivo evidenzia un progressivo aumento dell’angolo di direzione rispetto al molare laterotrusivo (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 73^\circ} ) e all’incisivo (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 85^\circ} ), fino al massimo valore rilevato nel condilo (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 180^\circ} ). Questo angolo, noto come angolo di svincolo mediotrusivo, si forma tra la cuspide centrale e quella distale del primo molare. La Tabella 4 e la figura 8 mostrano le distanze tra i punti del tracciato e il punto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1M_m} .

Tabella 4
Tracciato mediotrusivo molare Markers Distanza (mm) Direzione Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X} Direzione dinamica Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Y}
Figura 4: Distanze tra i punti mediotrusivi molari
Figura 8: Markers rilevati dal 'Replicator' durante la masticazione sul lato destro. 		2 0.68 Retrusiva Medializzazione
3 2.19 Retrusiva Medializzazione
4 3.22 Retrusiva Medializzazione
5 5.79 Protrusiva Medializzazione
6 7.22 Protrusiva Inversione
7* 4.81 Retrusiva Lateralizzazione
8 1.18 Retrusiva Lateralizzazione

La distanza lineare tra il punto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1M_m} e Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7M_m} è stata calcolata come Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4.81 \, \text{mm}} , con un angolo approssimativo di Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta = 91.33^\circ} . Info.pngCalcolo dettagliato: Vettori: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{1M_m7M_m} = (818.8 - 910.7, -855.1 - (-856.2)) = (-91.9, 1.1)} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{1M_mR_p^+} = (912 - 910.7, -741.2 - (-856.2)) = (1.3, 115)} . Norme: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |\vec{1M_m7M_m}| = \sqrt{(-91.9)^2 + (1.1)^2} \approx 91.92} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |\vec{1M_mR_p^+}| = \sqrt{(1.3)^2 + (115)^2} \approx 115.02} . Prodotto scalare: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{1M_m7M_m} \cdot \vec{1M_mR_p^+} = (-91.9 \cdot 1.3) + (1.1 \cdot 115) = -119.47 + 126.5 = 7.03} . Coseno: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cos(\theta) = \frac{7.03}{91.92 \cdot 115.02} \approx 0.000665} . Angolo: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta = \arccos(0.000665) \approx 90^\circ} .

Condilo Mediotrusivo

Il calcolo dell’angolo tra i segmenti Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1M_c - 7M_c} e Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1M_c - R_p^c} è fondamentale per analizzare i movimenti articolari nel sistema masticatorio. Questa analisi consente di comprendere come si muovono i segmenti articolari rispetto a un punto di riferimento. ( Figura 9, tabella 5)

Tabella 5
Tracciato masticatorio Markers Distanza (mm) Direzione Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X} Direzione Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Y}
Figura 5. finale.jpg
Figura 9: Markers rilevati dal 'Replicator' durante la masticazione sul lato destro nell'area incisale. 		2 2.13 Protrusiva Medializzazione
3 6.19 Protrusiva Medializzazione
4 10.70 Protrusiva Medializzazione
5 11.09 Protrusiva Inversione
6 6.09 Protrusiva Lateralizzazione
7* 2.61 Protrusiva Lateralizzazione
8 0.50 Protrusiva Lateralizzazione

La distanza tra il punto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1M_c} e Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7M_c} è risultata Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6.88 \, \text{mm}} , con un angolo calcolato di Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta = 166^\circ} . Sottraendo da Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 180^\circ} , si ottiene un angolo di Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 14^\circ} , noto come Angolo di Bennett. Per il calcolo dettagliato Info.pngCalcolo sintetico: Vettore: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{AB} = (-15.9, -60.4)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{AC} = (0.2, 52.5)} . Prodotto scalare: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{AB} \cdot \vec{AC} = -3172.62} . Norme: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |\vec{AB}| = 62.93} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |\vec{AC}| = 52.50} . Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cos(\theta) = \frac{-3172.62}{62.93 \cdot 52.50} \approx -0.971} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta = \arccos(-0.971) \approx 166^\circ} .

Discussione sulla rototraslazione condilare

Il moto rototraslazionale dei condili è cruciale per comprendere la cinematica mandibolare. Se i condili ruotassero attorno a un punto fisso, i tracciati dei molari e degli incisivi sarebbero semplici archi di cerchio. Tuttavia, i movimenti reali includono sia rotazione che traslazione.[1][2]

Durante la laterotrusione, il condilo ipsilaterale combina rotazione attorno all’asse verticale e traslazione laterale, mentre il condilo mediotrusivo si muove principalmente in direzione mediale e anteriore, generando il "Tragitto orbitante".

Descrizione matematica

La rototraslazione del condilo laterotrusivo può essere rappresentata come:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_m = x_{m0} \cos(\theta) - y_{m0} \sin(\theta) + T_x } Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_m = x_{m0} \sin(\theta) + y_{m0} \cos(\theta) }

Dove:

  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x_{m0}, y_{m0})} : posizione iniziale del molare ipsilaterale.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_x} : traslazione laterale lungo l’asse Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} .
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x_m, y_m)} : posizione finale.
Figura 10a: Rappresentazione di una conica.

Man mano che il condilo si muove, le coordinate Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x_m, y_m)} descrivono una traiettoria ellittica proiettata su un piano 2D. Questo avviene perché il centro di rotazione istantaneo del condilo non è fisso ma si sposta continuamente.

Un fenomeno simile si osserva per il condilo mediotrusivo e gli incisivi, le cui traiettorie sono influenzate da traslazioni mediali e anteriori e da rotazioni attorno all’asse verticale. Questi tracciati non sono ellissi perfette, ma curve più complesse a causa delle variazioni nei movimenti condilari.

I tracciati dentali sono correlati ai movimenti dei condili e offrono preziose informazioni sulla cinematica mandibolare, per cui sarebbe auspicabile spendere qualche parola in più sulla velocità del moto masticatorio e la rappresentazione di questa cinematica mandibolare in un forma geometrico/matematica chiamata 'Conica'.

Rappresentazione in una 'Conica'

Un modello basato su una conica passante per cinque punti strategici aiuta a rappresentare meglio queste traiettorie, come illustrato nella figura 10a.

In sintesi, i tracciati dei molari e degli incisivi assumono forme ellittiche complesse, poiché il centro di rotazione condilare si sposta continuamente. Questo modello aiuta a comprendere meglio la complessità dei movimenti mandibolari.

  1. ↑ T Ogawa 1, K Koyano, T Suetsugu Correlation between inclination of occlusal plane and masticatory movement.. J Dent. 1998 Mar;26(2):105-12. doi: 10.1016/s0300-5712(97)00001-8.
  2. ↑ W R Scott. Application of "cusp writer" findings to practical and theoretical occlusal problems. Part I.. I Prosthet Dent. 1976 Feb;35(2):211-21. PMID: 55483, DOI: 10.1016/0022-3913(76)90282-1
Retrieved from "https://www.masticationpedia.org/index.php?title=Store:Asse_Cerniera_Verticale_parte_2&oldid=20645"