It is well known that, in the all kinds of practical parting methods of sheet-metals, the shearing with the punch and die is the most suitable for the production of precision machine parts. But this shearing phenomenon is very complicated, so the theoretical studies of this phenomenon have been very few. In order to make clear the shearing phenomenon, the author studied the stress distribution in the sheared materials in the neighbourhood of cutting edges, and discussed the shearing characters. It is very difficult to analyse exactly the shearing mechanism, so the author tried to simplify the shearing phenomenon by assuming that the sheared material is plastic-rigid and plane-strained. Thus the author introduced a few networks of slip lines, by which some well known shearing characters can be explained.
On the other hand, the author proposed a new shearing model, that is, simple shearing deformations occur continuously in the thin straight layer containing the edges of punch and die. By this shearing model, the most of actual shearing characters can be explained easily, and the, shearing resistances of actual sheet-metals can be calculated from the stressstrain curves, the error of this calculation being within about ± 10% for the most actual sheet-metals. For example, the calculated shearing resistance of 1.0mm thick brass-plate is 32.3kg/mm², at the clearance of 7 % of sheared plate-thickness, the actual measured being 31. 9kg/mm², and the calculated value is 31. 7kg/mm² at the clearance of 12%, the measured being 31.0kg/mm².

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In this report the measurements of dividing error in gear are analysed by means of statistical methods. It is conventional that such data are plotted in the graph and the dividing accuracy is expressed by the difference between the maximum and minimum values in the graph. Where the number of teeth is large, the measurements of all teeth may reduce measuring accuracy. In such a case the measurements are made at every several pitches. So the dividing accuracy should be expressed, taking into consideration the measuring error and the dividing error of the teeth which have not been measured. This report treats such problems and presents a new expression of dividing accuracy based on the concept of "Confidence limits".

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The theory of cutting is applied to the study on the grinding mechanism. The grinding model which defines the mechanism of the plastic deformation of chip in grinding is presented. Experiments with single grains and diamond pyramids show the validity of the grinding model.
The effects of grinding speed and depth of cut on grinding forces and shear angle are investigated.
Further attempt in this paper is to find limitations of the application of the cutting theory. Owing to the swell-out residual at the track of a grain the grinding model is not explicitly correct. Experiments reveal that the swell-out residual decreases with the increase of grinding speed. This phenomenon is discussed from the standpoint of Kármán's plastic wave in workpiece.

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Rubbing the surface of carbon steel with the steel ball electro-plated with Radioactive zinc ⁶⁵Zn, minute wear amount was measured by measuring the radioactivity of rubbing surface. Wear mechanism of metal, especially the effect of roughness of rubbing surface and lubricating oil on wear was examined. These results indicated that wear remarkably increased with increasing the roughness of rubbing surface. These also showed that not only the adhesion of rubbing surface but the effect of scratch is severe in mechanical wear. If the coefficient of friction in boundary lubrication becomes smaller, wear was proved to be strikingly reduced. Minute mechanism of wear was searched for by auto-radiography. And the effect of the roughness of rubbing surface and lubrication on the distributions of size of wear particles was examined.

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