Active design of tooth profiles using parabolic curve as the line of action

This paper proposes a method for the design of gear tooth profiles using parabolic curve as its line of action. A mathematical model, including the equation of the line of action, the equation of the tooth profile, and the equation of the conjugate tooth profile, is developed based on the meshing theory. The equation of undercutting condition is derived from the model. The influences of the two design parameters, that present the size (or shape) of the parabolic curve relative to the gear size, on the shape of tooth profiles and on the contact ratio are also studied through the design of an example drive. The strength, including the contact and the bending stresses, of the gear drive designed by using the proposed method is analyzed by an FEA simulation. A comparison of the above characteristics of the gear drive designed with the involute gear drive is also carried out in this work. The results confirm that the proposed design method is more flexible to control the shape of the tooth profile by changing the parameters of the parabola.

Calcium, vitamin D, casein and whey protein intakes and periodontitis among Danish adults

Objective: To investigate whether intakes of Ca, vitamin D, casein and whey are associated with periodontitis and to investigate the possibility of interactions between them. Design: Cross-sectional study. An Internet-based, 267-item FFQ was used to assess dietary intake. Intakes of casein (32·0 g/d), whey proteins (9·6 g/d) and vitamin D (5·8 μg/d) were classified as within v. above the 50th percentile. Ca intake was classified as within v. below age-specific recommendations. Severe periodontitis was defined as having ≥2 inter-proximal sites with clinical attachment loss ≥6 mm (not on the same tooth) and ≥1 inter-proximal site with pocket depth ≥5 mm. Since vitamin D influences Ca absorption, models were stratified by lower and higher (<5·8 v. ≥5·8 µg/d) vitamin D intake. Setting Danish Health Examination Survey (DANHES) 2007–2008. Subjects Adult participants (n 3287) in the oral health study of DANHES 2007–2008. Results Intakes of Ca within recommendations (OR=0·76; 95 % CI 0·58, 0·99), whey ≥9·6 g/d (OR=0·75; 95 % CI 0·58, 0·97) and casein ≥32 g/d (OR=0·75 95 % CI 0·58, 0·97) were associated with lower likelihood of severe periodontitis after adjustment for age, gender, education, smoking, sucrose intake, alcohol consumption, number of teeth, daily brushing, regular visits to the dentist and chronic illness, irrespective of vitamin D intake levels. Intake of vitamin D alone was not associated severe with periodontitis. Conclusions Intakes of Ca, casein and whey protein were inversely associated with periodontitis. Consumption of foods rich in Ca, casein and whey (e.g. dairy foods) should be promoted, as they may contribute to the prevention of periodontitis. Further longitudinal studies are required to confirm these associations.

Calcium, vitamin D, casein and whey protein intakes and periodontitis among Danish adults

OBJECTIVE: To investigate whether intakes of Ca, vitamin D, casein and whey are associated with periodontitis and to investigate the possibility of interactions between them. DESIGN: Cross-sectional study. An Internet-based, 267-item FFQ was used to assess dietary intake. Intakes of casein (32.0 g/d), whey proteins (9.6 g/d) and vitamin D (5.8 mug/d) were classified as within v. above the 50th percentile. Ca intake was classified as within v. below age-specific recommendations. Severe periodontitis was defined as having >/=2 inter-proximal sites with clinical attachment loss >/=6 mm (not on the same tooth) and >/=1 inter-proximal site with pocket depth >/=5 mm. Since vitamin D influences Ca absorption, models were stratified by lower and higher (<5.8 v. >/=5.8 microg/d) vitamin D intake. SETTING: Danish Health Examination Survey (DANHES) 2007-2008. SUBJECTS: Adult participants (n 3287) in the oral health study of DANHES 2007-2008. RESULTS: Intakes of Ca within recommendations (OR=0.76; 95 % CI 0.58, 0.99), whey >/=9.6 g/d (OR=0.75; 95 % CI 0.58, 0.97) and casein >/=32 g/d (OR=0.75 95 % CI 0.58, 0.97) were associated with lower likelihood of severe periodontitis after adjustment for age, gender, education, smoking, sucrose intake, alcohol consumption, number of teeth, daily brushing, regular visits to the dentist and chronic illness, irrespective of vitamin D intake levels. Intake of vitamin D alone was not associated severe with periodontitis. CONCLUSIONS: Intakes of Ca, casein and whey protein were inversely associated with periodontitis. Consumption of foods rich in Ca, casein and whey (e.g. dairy foods) should be promoted, as they may contribute to the prevention of periodontitis. Further longitudinal studies are required to confirm these associations.