How to calculate the radius of a rounding. Variable radius fillets

When creating layouts in Photoshop, designers love to use rounded corners for a variety of blocks.

Moreover, they have always loved to do this, since time immemorial. No doubt, blocks with such angles look much nicer, which in a positive way affects the design of the site itself.

But it’s not entirely easy for a layout designer in this situation. How to convey this rounding of corners in code? Previously, before the advent of CSS3, they got out of the situation in a time-consuming and painstaking way - they cut out rounded corners from the image and inserted them into the code as background images.

But then CSS3 appeared and things became much easier, since this specification has a property specifically created for drawing round corners on blocks. It's called

,

1

-moz

, , For example.

But how can you recognize it? Don't call the designer with a question - what radius did you include in the layout?

I will say that I did not immediately receive an answer to this question. Out of habit, I went to the forum forum.htmlbook.ru, but didn’t get anything specific from there. After searching on the Internet, a solution was found. And it turned out to be very simple.

Let's scale the layout so that the rounded corner of the block is clearly visible. We see in it how the straight line of the block smoothly turns into a rounding, which after its completion again turns into a straight line. We are interested in two points here - where the rounding begins and where it ends. Let's call them tangent points:

Let's draw two guides as auxiliary lines - vertical and horizontal. In the figure they are shown as thin blue lines. We will need them in order to obtain the point of their intersection. Then select from the Photoshop toolbar rectangular selection(Rectangular Marqee).

And build a square (holding the Shift key) so that its left top corner coincided with the intersection point of the guides. Let's drag it out with the mouse so that the sides of the expanding square coincide with the tangent points mentioned earlier. As soon as the lines of the square and the tangent points coincide, release the mouse - the construction is completed.

You can build in another way. Start the selection from one point (tangent) and end at another, that is, as if diagonally. The result will be the same, but you don't need to create guides:

Now let’s open the “Info” panel and take a look at the dimensions of the constructed square. The lengths of the sides will be the rounding radius for this block on the layout:

Don't believe me? This is for sure - any of the sides of the constructed square will be the radius of this fillet! To clarify a little more, I drew a circle in AutoCAD with a radius

so as to fit its upper right corner into the center of the created circle. The figure clearly shows that any of its sides is the radius of the circle in which it is inscribed:

When constructing a selection square on a PSD layout, it happens that it is impossible to accurately get the sides of the square to coincide with the guideline. I found such a way out for myself. Well, it didn’t hit, it didn’t hit.

I build a square further. Once it's built and the mouse is released, I simply move the selection to Right place using the arrow keys on your keyboard. And then everything is as before. I look at the “Info” panel and get the exact rounding radius:

As you can see, everything turned out to be very simple. Now knowing exact value rounding radius, you can create a website template that best matches the PSD layout.

P.S.

There is an inaccuracy in the drawing of a circle and square created in AutoCAD. The callout indicates that a rectangle has been built, although in fact it is, of course, a square.

Why is the rounding radius equal to

1

40px

, and in AutoCAD -

1

41px

? Yes, I just missed when I was drawing a circle. This does not change the essence of the matter, it only shows even more clearly the correctness of the approach.

As you know, all devices, machines, mechanisms and devices consist of certain parts. Each of them, in turn, has several parts that have a strictly defined purpose. In technology they are called parts elements, and they include, for example, chamfers, fillets, grooves, threads, etc.

Many parts used as components machines and mechanisms and manufactured both from metals and from various plastics, have roundings and chamfers. These elements are characterized sizes and radii, which are established by such a document as GOST 10948-64. It contains a data table with parameters roundings and chamfers which must necessarily comply with the standard.

GOST 10948 – 64

Standard dimensions of chamfers and radii
1st row	2nd row	1st row	2nd row	1st row	2nd row	1st row	2nd row
0.10	0.10	1.0	1.0	10	10	100	100
-	0.12	-	1.2	-	12	-	125
0.16	0.16	1.6	1.6	16	16	160	160
-	0.20	-	2.0	-	20	-	200
0.25	0.25	2.5	2.5	25	25	250	250
-	0.30	-	3.0	-	32
0.40	0.40	4.0	4.0	40	40
-	0.50	-	5.0	-	50
0.60	0.60	6.0	6.0	63	63
-	0.80	-	8.0	-	80

fillets in technology it is customary to call those fillets, which are often located on the inside and corners of various machine parts. This word is of German origin, and when translated into Russian it means “ recess», « groove" The use of fillets greatly facilitates and simplifies the production of various parts using such common technological processes, such as forging, stamping and casting. In addition, their use significantly improves the strength characteristics of axles and shafts in those places where the transition from one diameter to another is made.

fillets often used in the design and manufacture of stepped shafts. In those places where their parts, having various diameters, they greatly increase the overall strength of the entire structure, and also reduce the concentration internal stresses materials.

In cases where fillet is inside the hole, then the size of the chamfer made on its edge is selected so that the surface chamfers And rounding did not touch each other.

fillets almost always used in the manufacture of engine crankshafts internal combustion, produced from high-strength cast iron, alloy and carbon steels. If the shaft is produced by casting, then it is usually hollow, and therefore the radii of the fillets, the thickness of the “cheeks”, and the diameters of the connecting rod and main journals are increased.

Chamfers are also one of the parts elements. If you look at the etymology of this word, it turns out that it has French origin: in the language of Voltaire and Hugo " faccete" means " beveled parts of the ribs or corner V". Chamfers designed primarily to dull too much sharp corners parts and, thereby, ensure the safety of personnel involved in the assembly of various machines and mechanisms, their operation, maintenance and repair.

Chamfers, as well as the parameters that they have, are usually depicted and indicated in the drawings in cases where this arises from the fact technical solution, which this or that part has. IN otherwise neither themselves chamfers, nor their parameters are indicated on the drawings, however, all sharp edges must be dulled directly on the parts being manufactured.

One of critical systems internal combustion engines is the gas distribution system, which largely determines the functioning of the units. To ensure normal gas exchange in them, it is necessary to achieve the closing and opening of the inlet and outlet openings, and in strictly in a certain order and at strictly defined intervals. For this purpose, special metal valves are used, which are driven by mechanisms designed for this purpose. One of the mandatory elements of valves are sealing chamfers: they ensure the unhindered escape of gases, as well as guaranteed sealing of the holes.

Curvature radii are prescribed to prevent the formation of shrinkage cracks that arise due to uneven crystallization (Fig. 13).

Fig. 13. The influence of the radius of the mating walls on the quality of castings.

In addition to the internal ones, external sharp edges are also matched to prevent the formation of cracks in the molds. Sharp edges are only allowed on parting planes. The size of the recommended internal and external radii of mating castings depends on the casting method:

Table 3. Dependence of rounding radii on the casting method.

Smooth transitions. To prevent the formation of cracks in the boundary zones during cooling of the casting, transitions from thick to thin sections should be made gradually (Fig. 14).

Rice. 14 Smooth transitions from thick to thin casting sections

The size of the mating section is determined by the ratio of wall thicknesses.

Slopes (taper) are necessary on surfaces located on the parting plane of the mold to ensure removal of the model (casting) from the mold. Slopes at internal surfaces more slopes on external surfaces (Fig. 15).

Rice. 15. Slopes on external and internal surfaces.

The amount of slope also depends on the casting method.

Table4. Dependence of slopes on casting method

Holes are always cast to prevent the opening of shrinkage cavities and porosity in a solid casting, to reduce the volume of subsequent processing, and to reduce mass. The minimum diameter and maximum hole length depend on the casting method and alloy.

Table 5. Dependence of hole parameters on casting method.

Casting method and alloy	Minimum diameter, mm	Hole depth to diameter ratio		Thread pitch	Thread diameter, mm
		non-through	end-to-end		outer	interior
Pressure alloy:
zinc
magnesium
aluminum
In one-time molds with wall thickness:

The distance from the hole to the edge of the cast part should be more than (Fig. 16) 1.2 d, where d is the diameter of the hole.

Rice. 16. Distance to the edge of the part.

Reinforcement is the process of pouring metal parts into the casting cavity to improve the properties of the casting. The metal parts being poured are called fittings and must have comparable shrinkage values ​​during cooling. Reinforcement is most widely used in injection molding to reduce the volume of subsequent assembly and to create special physical properties(pouring copper coolant circulation tubes, pouring bronze bushings into the zinc alloy body reduces friction) or to eliminate shrinkage cavities. (Fig. 17)

Creates a fillet with variable radius values. Use checkpoints for more simple definition rounding.

Example of control points for variable radii
No control points
Control points for variable radii	With control points

Round elements

Some fields that allow you to enter numeric values ​​allow you to create an equation by entering an equal sign (=) and selecting global variables, functions, and file properties from a drop-down list. See Entering equations directly.

		In the graphics area, select the objects you want to fillet.
	Spread along transition lines	The fillet applies to all faces tangent to the selected face. Example: Spread Along Transition Lines
	Full preview viewing	Displays a preview of the fillet of all edges.
	Partial preview viewing	Displays a preview of the fillet on one edge only. Press A to preview each fillet one by one.
	No prev. viewing	Reduces the time it takes to rebuild models with complex surfaces.

Change settings. radius

	Radius	Sets the radius of the fillet.
	Attached radii	List of edge vertices selected in the section Round elements, for parameter Edges, edges, elements and loops, as well as a list of control points selected in the graphics area.
	Configure unspecified	Apply the current radius to all elements that do not have radii assigned in the section Attached radii.
	Set up everything	Apply the current radius to all elements in the section Attached radii.
	Number of copies	Specifies the number of control points on the edges.
	Smooth transition	Creates a fillet that changes smoothly from one radius to another as the fillet edge matches the adjacent face.
	Linear transition	Creates a fillet that varies linearly from one radius to another without matching the tangency of the edge to the adjacent fillet.

Options for reduced fillet

Using these options, you can create a smooth transition between adjacent surfaces, including the edge of a part, at a fillet corner. You can select a vertex and radius, and then assign the same reduced fillet distances to each edge. The reduced distance is the point along each edge where the fillet begins into three edges that meet at one vertex. Example: Preview of a reduced fillet

Before you ask Options for reduced fillet, In chapter Round elements follow these steps:

	Distance	Sets the reduced fillet distance measured from the vertex.
	Reduced fillets	Select one or more vertices in the graphics area. The edges of the reduced fillets are connected at the selected vertices.
	Distance	List of edge numbers with corresponding reduced distance values. To apply different reduced distances to edges, select an edge in the Reduces box. Then set the distance and press the Enter key.
	Configure unspecified	Applies the current distance to all edges that do not have distances assigned in the Distance section.
	Set up everything	Applies the current distance to all edges in the Distance section.

Fillet Options

Select through edges	Allows you to select edges through the faces that these edges hide.
Floor type	Controls the behavior of fillets on individual closed edges (for example, circles, splines, ellipses) when connecting to edges. Example: Floor type. Select one of the following options:

Curvature radius

Standing near one of these curves, could you determine the value of its radius? It's not as easy as finding the radius of an arc drawn on paper. In the drawing, the matter is simple: you draw two arbitrary chords and construct perpendiculars from their midpoints: at the point of their intersection lies, as is known, the center of the arc; its distance from any point on the curve is the required length of the radius.

But to make a similar construction on the ground would, of course, be very inconvenient: after all, the center of the circle lies at a distance of 1-2 km away from the road, often in an inaccessible place. It would be possible to carry out the construction on the plan, but removing the curves on the plan is also not an easy job.

All these difficulties are eliminated if we resort not to construction, but to calculation of the radius. To do this, you can use the following technique. Let's add (Fig. 84) mentally the arc AB rounding to a circle. Connecting arbitrary points C andD rounding arcs, measure the chord CD, and also "arrow" E.F. (i.e., segment height CED). Using these two data, it is no longer difficult to calculate the required length of the radius. Looking at straight lines CD and the diameter of the circle as intersecting chords, we denote the length of the chord by A, the length of the arrow through h, radius through R; we have:

and the required radius 1)

For example, with an arrow at 0.5 m and chord 48 m required radius

This calculation can be simplified by considering 2 R-h equal 2 R - liberty is permissible, since h is very small compared to R (after all R- hundreds of meters, and h - units of them). Then we get a very convenient approximate formula for calculations:

Applying it in the case now considered, we would obtain the same value

R = 580.

Having calculated the length of the radius of curvature and knowing, in addition, that the center of the curvature is perpendicular to the middle of the chord, you can approximately outline the place where the center of the curved part of the road should lie.

If rails are laid on the road, then finding the radius of curvature is simplified. In fact, by pulling the rope tangentially to the inner rail, we obtain a chord of the arc of the outer rail, the arrow of which h (Fig. 85) is equal to the track width - 1.52 m. The radius of curvature in this case (if a is the length of the chord) is approximately equal to

At a=120m the radius of curvature is 1200 m 2).

1) The same could be obtained in another way - from right triangle COF, Where O.C.= R, CF=a/2,OF= R - h,

According to the Pythagorean theorem

2 ) In practice, this method presents the inconvenience that, due to the large radius of curvature, the rope for the chord requires a very long one.

Rice. 85. To calculate the radius of a railway curve