Introduction

In engineering practice, it is often required to make a drawing that shows the interior details of the object. If the object is simple in its construction, the interior portion of the object can be easily interpreted by dotted lines in the orthographic projections. When the dotted lines of hidden parts are too many, the views become confusing and hard to read. In such cases, views can be drawn by cutting the object by an imaginary cutting plane so as to expose its interior or hidden details. The part of the object between the cutting plane and the observer is assumed to be removed so as to show the internal constructional features or details of the invisible surface. The exposed interior details are drawn in continuous thin lines instead of dotted lines. Such views are known as sectional views or views in section. The section surfaces are indicated by section lines, evenly spaced and inclined at 45° to the reference line.

Section Planes

These are generally perpendicular planes. These may be perpendicular or parallel to one of the principal planes and either perpendicular, parallel or inclined to the other plane. These planes are usually described by their traces.

Sections

Basically, sections are of two types:

• (i) Apparent Section

• (ii) True Section

• (i) Apparent Section:The projection of the section on the principal plane to which the section plane is perpendicular is a straight line coinciding with the trace of the section plane on it, whereas its projection on the other plane to which it is inclined is called apparent section.

• (ii) True Section:The projection of the section on a plane parallel to the section plane shows the true shape of the section. When the section plane is parallel to the HP or ground plane, the true shape of the section is seen in the sectional top view. When it is parallel to the VP, the true shape is projected in the sectional front view.

But when the section plane is inclined to one of the principal planes, the section has to be projected on an auxiliary plane parallel to the section plane to obtain its true shape.

When the section plane is perpendicular to both the principal planes, the sectional side view shows the true shape of the section.

This definition is a good starting point. However, for the purposes of this book, it needs some further clarification. Indeed, the expression European Company Law (hereafter ‘ECL’) requires one to focus on the meaning of both ‘company’ and ‘company law’, on the one hand, and on the qualification ‘European’, on the other.

One or more founders may decide to form a new company (NewCo) for carrying out a business activity.

Introduction

Drawing is a graphic language by which communication is accomplished through sketches (drawings). Drawings can be of various types. If compared with verbal or written description, drawings provide a far better idea about the shape, size and appearance of any object or situation or location, that too fairly quickly. From a manufacturing point of view, 2D and 3D drawings are very important and commonly used in engineering industry. Drawings are prepared manually or by using a computer. In 2D view (orthographic projection), one view is not enough to get all the details of the object. So it is necessary to draw the front view, top view, bottom view, right side view and left side view.

To be more useful, in particular from the manufacturing point of view, the sketch or drawing should include dimensions, manufacturing details, materials used, etc. Drawing equipment and instruments are needed to record information on drawing paper or any other suitable surface. Drawing, mainly consisting of straight lines, curves, circles and arcs, is prepared with certain instruments. The quality of the drawing mainly depends on the quality of the instruments, their adjustment, handling and care. Therefore, the equipment must be reliable and accurate, as the same will result in good quality drawing, which will further enhance a student's interest. The correct selection and use of pencils and drawing instruments should be taught throughout the course. Beginners certainly need guidance on the selection and purchase of the drawing instruments and equipment essential for drafting. The various instruments and other drafting equipment are described below.

List of Draughting Tools

The following is the list of draughting tools which every student must possess:

1. Drawing Board

2. Mini-Draughter

3. Small Instrument Box, containing the following:

• • Large Size Compass

• • Small Bow Compass

• • Large Size Divider

• • Small Bow Divider

4. Set-Squares

5. Set of Scales

6. Protractor

7. French Curves

8. Drawing Sheets

9. Drawing Pencils

10. Paper Fasteners

11. Pencil Sharpener

12. Sand Paper Pad

13. Eraser

14. Duster

Some of these have been explained in greater detail in the subsequent sections.

Drawing Board

A drawing board is usually made of well-seasoned soft wood. To prevent warping, narrow strips of wood are glued together.

Introduction

Although a pictorial view helps in understanding the shape of the object, however it suffers from the drawback that it fails to convey the actual size and inner details of the object. This is because a pictorial view is drawn by seeing the object, as a three directional task. However, for design purpose, it requires the actual details of the object. For this purpose, the pictorial view of the object is converted into orthographic views by applying the principles of orthographic projections. Conversion of a pictorial view into the orthographic view requires sound knowledge of the principles of pictorial projection and some imagination.

Direction of Sight

For converting a pictorial view of an object into orthographic views, the direction from which the object is to be viewed for its front view is generally indicated by means of an arrow. The arrow must be parallel to the sloping axis. If there is no arrow, the direction for the front view may be decided to give the most prominent view; other views are drawn by looking in the directions perpendicular to the first direction.

Orthographic Views

Orthographic views can be drawn by two methods:

• (i) First-Angle Projection Method

• (ii) Third-Angle Projection Method

First-Angle Projection Method

In the first-angle projection method, the object lies in the first quadrant, i.e., above the HP and in front of the VP. The object lies in between the observer and the plane of projection. In this method, when the views are drawn in their relative positions, the top view is placed below the front view and the left side view is placed to the right side of the front view. Thus in the first-angle projection method, either of the side views is so placed that it represents the side view of the object away from it, as shown in Fig. 17.1.

In the same way as discussed above, three more views may be obtained by placing the plane of projection on the front, top and left hand side of the object. The three views then obtained are called rear or back view, bottom view and right side view, respectively. The layout of all the six views on the drawing sheet is shown in Fig. 17.2.

During the formation of the acquis on the freedom of establishment, the European Commission promoted discussion (see, § 7.3) of the adoption of legislative tools able to enhance cross-border mobility for companies and firms, in particular by permitting a company to transfer the seat with a view to changing the applicable company law (lex societatis), without going into liquidation.

Introduction

Three views of an object, viz. the front view, top view and side view, are sometimes not sufficient to provide complete information regarding true shape and size of an object. Additional views are therefore projected on other planes (auxiliary planes) and are known as auxiliary views or auxiliary projections.

Types of Auxiliary Planes and Views

Auxiliary planes are of two types:

• (a) Auxiliary Vertical Plane (AVP)

• (b) Auxiliary Inclined Plane (AIP)

Auxiliary vertical plane (AVP):Auxiliary vertical plane (AVP) is perpendicular to the HP and inclined to the VP. The projection on an AVP is called an auxiliary front view. See Fig. 11.1.

Auxiliary inclined plane (AIP):Auxiliary inclined plane (AIP) is perpendicular to the VP and inclined to the HP. The projection on an AIP is called an auxiliary top view. See Fig. 11.2.

For showing the orthographic projections of an object, the auxiliary plane should always be rotated about the plane to which it is perpendicular.

Projections of Points

(a) Projection of a point on an auxiliary vertical plane (AVP):A point A is situated above HP and in front of the VP. AVP is a plane perpendicular to the HP and inclined to the VP. The HT of this plane is inclined to x-y and VT perpendicular to x-y line. The HP and the AVP meet at right angles in the line x1 y1. From the Figs. 11.3 (a) and 11.3 (b), the following points may be observed:

• (i) The distance of the auxiliary front view from x1y1 is equal to the distance of the front view from x-y, which in turn is the distance of the point A from the HP.

• (ii) The line x1 y1 is inclined to x-y at an angle ϕ, which is the angle of inclination of the AVP with the VP.

To draw the orthographic projections, see Fig. 11.3 (c).

• (i) Draw the reference line x-y and mark the front view a’ and the top view a.

• (ii) Draw a new reference line x1 y1, making an angle ϕ with x-y.

Adoption of the majority principle as a general rule requires adequate consideration of minority shareholders’ interest. In this respect, ECL provides many rules aiming at protecting minority shareholders, such as: reinforced majorities for some fundamental matters, anti-dilution tools in case of a capital increase, double majorities for decisions affecting special classes of shares (or special consent of the affected shareholders), sterilisation of voting rights attached to treasury shares, and so on.

Introduction

In this chapter, an attempt is being made to introduce the readers to the projection of points. Following the treatment here it will be easy for them to understand the projection of lines, planes and solids in the subsequent chapters. For the projection of points, the quadrant system is considered and a point lying in space is assumed in any one of the four quadrants that are obtained by the intersection of two principal planes. A point can lie with reference to both the reference planes, i.e., HP and VP. Its projections are obtained by extending projectors perpendicular to the planes.

In order to obtain the projection of a point lying in three-dimensional space on a two-dimensional plane (drawing sheet), the principal plane HP is rotated clockwise through 90° and made co-planner with the VP. This process coverts the three-dimensional quadrant system into two-dimensional front and top views, i.e., the front view VP is obtained above x-y line where this x-y line represents the elevation or front view of HP; similarly the top view of HP is obtained below the x-y line, here the x-y line represents the top view of VP.

Projection of a Point Lying in the First Quadrant

The pictorial view Fig. 8.1(a) shows a point A lying in the first quadrant, i.e., above the HP and in front of the VP. When the point is viewed in the direction of l, the view from front a’ is obtained as the intersection point between the ray of sight through A and the VP. When the point is viewed in the direction m, the top view (a) of point ‘A’ is obtained as the ray of sight intersect with HP at a. Similarly front view (a’) of ‘A’ is obtained when the ray of sight coming from l direction intersects VP at a'. Hold VP and rotate HP 90° in the clockwise direction; these projections are seen in the Fig. 8.1(b). The front view a’ is above x-y and top view below it.

The line joining a’ and a (which is called as projector) intersects x-y at right angle (90°) at a point a.

An important chapter of EU company law includes annual and consolidated accounts. The following paragraphs will offer a brief overview of Directive 2013/34/EU, and in particular will focus on: (a) the annual accounts layouts, the management report and the duty of publication; (b) the accounting principles; (c) the consolidated accounts. Information will also be given on the IAS/IFRS accounting principles, as well as on statutory audits.

As mentioned, the concept of corporate governance includes the system by which companies are directed and controlled. In Europe different board structures coexist as, depending on the country, companies may put in place either a ‘one-tier’ or ‘single board’ system (also called ‘monistic’ or ‘unitary board’ system), a two-tier (or ‘dual board’ or ‘dualistic’) system, or some form of mixed system. The EU acknowledges the coexistence of these board structures, which are often deeply rooted in the country’s overall economic governance system, and has no further intention of challenging or modifying this arrangement.

Introduction

Planes or surfaces are objects that have two dimensions, i.e., length and breadth; they have negligible thickness. Plane surfaces may be considered of infinite sizes. However, for convenience, segments of planes are only considered in the solutions. Planes are represented in space by either of the following:

• • Three non-collinear points, Fig. 10.1(a)

• • A line and a point, Fig. 10.1(b)

• • Two intersecting lines, Fig. 10.1(c)

• • Two parallel lines, Fig. 10.1(d)

• • A plane, Fig. 10.1(e)

Types of Planes

Planes are mainly of two types:

• • Principal Planes

• • Secondary Planes

Principal planes:The planes on which the projections are obtained are called the principal planes. Examples of principal planes are horizontal and vertical planes.

Secondary planes:Secondary planes are of two types:

• (i) Perpendicular planes

• (ii) Oblique planes

(i) Perpendicular planes: These planes can be divided into the following sub-types:

1. Perpendicular to both the principal planes

2. Perpendicular to one of the principal planes and parallel to the other plane

3. Perpendicular to one of the principal planes and inclined to the other plane

1. A plane perpendicular to both the principal planes.A square plane ABCD is perpendicular to both the principal planes. Its horizontal trace (HT) and vertical trace (VT) are in a straight line perpendicular to the reference line x-y, as shown in Fig. 10.2. The elevation, b'c', and plan, ab, of the square are both straight lines coinciding with VT and HT, respectively, i.e., VT and elevation, HT and plan overlapping.

2. Perpendicular to one of the principal planes and parallel to the other plane.

• (a) A plane perpendicular to HP and parallel to the VP. A square lamina ABCD is perpendicular to the HP and parallel to the VP. Its HT, is parallel to x-y and it has no VT. The front view a'b'c'd’ shows the true shape and size of the square object. The top view ab is a line, parallel to x-y, coinciding with HT, as shown in Fig. 10.3.

• (b) Plane, perpendicular to VP and parallel to the HP. A square ABCD is perpendicular to the VP and parallel to the HP. Its VT is parallel to x-y and it has no HT. The top view abcd shows the true shape and size of the square object. The front view d'c’ is a line, parallel to x-y, coinciding with VT, as shown in Fig. 10.4.