of MP 
^ M-vector 
en the lower 
] vectors of each 
denote I-vector 
de 
n cycle 
of the denture 
f the movement. 
duration from 
  
the opposite side. To eliminate the interference by lip 
functions, they were instructed to keep their lips open during 
mastication. 
32 Mandibular Movements 
The mandibular movements were classified into two types in 
the frontal view by its direction at the time when the upper 
denture began to sink(Fig. 5). One was the type of normal 
stroke (the path of closure was on ipsilateral working side of 
mastication : IS) and the other was reversed (the path of 
closure was on contralateral side : CS). 
33 Data Transformation 
The transformed representative points from the measured 
targets were followed: the incisal point and the top of 
mesiolingual cusps of first molars in upper dentures; the 
incisal point and the central pits of first morals in lower 
dentures(Fig. 6). 
The plane which contains the three points on the upper 
denture was defined as the upper occlusal plane(UP), and the 
centroid calculated with these points was defined as the 
centroid of the upper denture(CU). Similarly the lower 
occlusal plane(LP) and the centroid of the lower denture(CL) 
were defined. And with the targets on the metal frame attached 
to the mandible, the mandibular plane(MP) and the centroid of 
the base of the mandible(CM) was defined.(Fig. 6) 
The vector directed from CL to the lower incisal point was 
defined as I- vector, and the vector from CM to the mentum 
was defined as M-vector. 
3.4 Measurement of the Denture Mobility 
The amount of the vertical denture mobility on the upper 
incisal points was defined as the distance between the 
beginning point of the sinking and the maximum point of 
displacement in one cycle. Lateral and antero-posterior(A-P) 
movements of the upper dentures were measured similarly on 
the basis of the timing when the incisal points of the upper 
denture began to sink(Fig. 7). 
The amount of vertical, lateral, and antero-posterior 
movements of each points on upper dentures were measured. 
And then, upper denture movements were investigated in the 
relation to the path of closure of the mandible. 
We investigated the movements of lower dentures about 
following points: 
1. Pitching on the lateral axes. The normal vector of LP was 
project to the plane containing the normal vector of MP and 
M-vector, and the inner products between the unit normal 
vector of MP and the unit normal vector of LP were 
investigated. 
2. Rolling on the A-P axes. I-vector was projected to the 
plane containing the M-vector and crossing MP at the right 
angles, and the inner products between the unit normal vector 
of MP and the unit normal vector of LP were investigated. 
3. Rotation on the vertical axes. I-vector was projected to 
MP, and the inner products between the unit I-vector and the 
371 
unit M-vector were investigated. 
Each inner products was investigated frame by frame (Fig. 8). 
Normal vector of LP 
I-vector 
LP 
  
Vertical axes 
  
  
  
Lateral axes 
A-P axes 
Fig. 8 Relation of the lower dentures’ movements and 
the reference planes. 
4. RESULTS 
4.1 Accuracy of the System 
A computer-controlled XYZ pulse stage was used to verify the 
accuracy of this system. One target on the pulse stage moved 
within the range of 20.0 mm cube along each axis at intervals 
of 5.0 mm, and all of 125 points were measured for calibration. 
The average of residuals’ square sum of 125 points’ coordinates 
from their real coordinates were calculated, and maximum 
residual was 0.3 mm. 
4.2 Denture Movements (Fig. 9 ) 
Table. 1 shows amounts of the upper denture mobility. 
In tapping, there was few lateral movements. The incisal 
points sank more than the molar points and both moved 
forward. Denture base pitched forward and upper. 
In mastication, dentures moved much more than in tapping. 
Analyzing sequential data on these 3 points, upper dentures 
intended to pitch upper and forward, and to incline toward the 
mastication side. In lateral movements, incisal points moved 
more than molar points. Denture base rotated and moved 
parallel at the same time. 
Table. 2 shows the results of the denture movements related 
to the path of closure of the mandible. 
5. CONCLUSION 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996