GB2124144A - Method of cross-cutting elongate pieces of timber and device for performing the method - Google Patents

Abstract

The distance n% between the retracted corner H of the root end part of a piece of timber 20 and a reference line L is measured by a device 30 and the result of the measurement is fed into an electronic unit 40 where a command signal is generated. The signal is fed to a setting means 16 by which a cross- cutting saw blade 12 is displaced relative to the piece of timber 20, or vice versa, to such an extent that the retracted corner H comes to lie in the cutting plane U of the saw blade 12. The device and method are used to achieve an exactly determined, extremely economical cross-cut of boards and planks which do not have any quality defects at the root end portion. <IMAGE>

Description

SPECIFICATION Method of cross-cutting elongate pieces of timber and device for performing the method This invention relates to a method of cross-cutting the root end of elongate pieces of timber, such as boards and planks, each having a top end and a root end, the latter, as a rule, terminated by an edge extending obliquely to the longitudinal axis of the piece and having as terminal points a projecting corner and a retracted corner. The invention also relates to apparatus for carrying out the method.

When cross-cutting timber, e.g. boards, to a desired length, generally a length fitting into an established system of longitudinal modules (where one module is, for example, equal to 3 dm), the cutting operation is commenced at the root end and the top end is cut off at a suitable whole multiple of longitudinal modules so that the board thus obtained fits into the module system. The fact that any cut at all is made at the root end is partly caused by the necessity to remove defects such as slots (clefts) or wanes present there, but chiefly and primarily it is necessary to achieve a clean and straight edge extending at right angles to the longitudinal axis of the piece of timber. The latter reason is often the only reason.

It will be readily understood that the cut-off portion at the root end should be as small as possible. As a matter of fact, the module system means that a cutoff at the root end which is unnecessarily too long, e.g. by 1 cm, may cause almost a whole 3 dm module (to be exact, a section of 29 cm) to be lost at the top end.

The root end is usually cut off from green (not dried) timber in a so-called green sorting or trimming plant, or in a so-called trimming plant where the boards are fed crosswise to a stationary circular saw blade. An operator stands a short distance upstream of this cross-cutting means and determines whether it is necessary or not to make a cut to remove defective portions at the root end. In the affirmative case, the operator pulls out the board so that the whole defective portion will be removed by the cut. As to the other boards, in most cases only a standard terminal adjustment is automatically made a short distance upstream of the cross-cutting means so that the portion which is cut off is of the same length in all boards.It will be understood that in such a case the cut-off length has to be dimensioned according to the boards having the most oblique terminal edge, i.e. the greatest distance in the longitudinal direction between the projecting corner and the retracted corner, although such boards in most cases are in minority. Consequently, on most boards in unnecessarily large portion is cut off.

It is an object of the present invention to provide a method and a device whereby the cut-off portion is minimized in pieces oftimberwhere obtention of a non-oblique terminal edge is the only reason for a cut at the root end.

With this object in view the present invention provides a method of cross-cutting the root end part of elongate pieces of timber, such as boards and planks, each having a top end and a root end and being, in an arbitrary longitudinal position, conveyed in transverse direction past a stationary, elongate measuring device, extending transversely or obliquely to the feed direction of the pieces of timber, and onwards to a cross-cutting saw blade, and, at some stage during their progress towards the saw blade, said pieces of timber each being displaced in their longitudinal direction until their respective root ends bear against a stop means, characterised in that with each piece of timber having at its root end a sloping edge limited by a retracted corner and a projecting corner, the distance in the longitudinal direction between the projecting and the retracted corner of each piece of timber is measured by the measuring device which generates signals which are fed into an electronic unit where a command signal, corresponding thereto, is generated and is fed to a displacement means to control said displacement means to displace in the longitudinal direction of each piece of timber either at least a part of said stop means, or the cross-cutting saw blade, until the retracted corner of each piece of timber lies in the cross-cutting plane of the cross-cutting saw blade, whereby waste at the cross-cut on the root end is minimized.

The invention also provides a device for carrying out the said method.

The invention will be described further by way of example, with reference to the accompanying drawings, in which: Figure I is a plan view of a first embodiment of the device of the invention; Figure 2 is a plan view of a second embodiment of the device of the invention; Figure 3 and Figure 4 are plan views, to a somewhat larger scale, showing how the measuring devices shown in Figures 1 and 2 operate; Figure 5 is a cross-section of a third embodiment of a measuring device; and Figure 6 is an operative block diagram of an electronic unit.

For parts with identical function identical or analogous reference characters are used in all drawing Figures.

In a first embodiment of the method of the invention, as performed by the device shown in Figure 1, a number of pieces of timber in the form of boards 20, 21 are carried by a cross-conveyor 10 which moves in direction R. The boards 20, 21 have been obtained by cutting up logs which in their turn have been obtained by long logs having been laid off into log lengths, i.e. having been cross-cut. The boards have plane faces a and b parallel one with the other, and side or longitudinal edges c, d, also parallel one with the other (see also Figure 5). In contradistinction thereto, a transverse edge eat the root end, and a transverse edge fat the top end are irregular, and, as a rule, not at right angles to any of the faces a to d.

The boards 20, 21 are carried by carrier means 11 arranged on the conveyor 10, whereby it is assured, among eitherthings, that the longitudinal axes and the side edges c, d of the boards 20, 21 always extend at right angles to the feed direction R.

Since the root end edge e is oblique relative the side edges c, d and the longitudinal axis x (which is parallel with the side edges), a projecting corner G and a retracted corner Hare present at the root end.

It will be understood from the drawing that a minimum cut-off portion at the root end will be obtained when the saw cut is directed along a plane Zwhich passes through the retracted corner H and is at right angles to the axis x.

Supposing that in the board 20 the greatest usable whole number multiple of a determined module measure, e.g. dm, will lie in a plane Vjust before a defective zone K at the top end, which zone K has in any case to be cutoff. If the cut-off at the root end were erroneously to be located in a planet', e.g.

only 15 mm beyond the corner H, the cutting plane at the top end would be displaced to a location V' which lies 15 mm within the defective zone K.

Consequently, the cut-off at the tope end would have to be displaced to a plane at the closest lower whole number multiple of the module measure m, and the whole zone M, comprising perfect wood would be wasted.

A cross cutting or bucking means in the form of a circular saw blade 12 having a cutting plane U, is located adjacent the conveyor 10. The saw blade 12 is mounted on the output shaft 14 of a motor 13 which is displaceable on guides 15a,15b in the direction Sat right angles to the feed direction R of the conveyor 10 and parallel to the axesxofthe conveyed boards 20, 21. Displacement of the motor 13 is effected by a double working, pressure fluid driven cylinder-piston-assembly 16 whose piston rod 1 6a is attached to motor 13. Instead of displacing the entire motor 13, which is rather heavy, the saw blade 12 alone may be displaceable in both directions of arrow S by action of assembly 16.

A measuring device 30 is provided upstream of the cross cutting means 12 to 15 and comprises a rectilinear measuring ramp 31 having a plurality of photodiodes or photoelectric cells 32. An additional photodiode 33 is mounted in front of the photodiodes 32 (i.e. upstream relative to the direction of movement R). All photodiodes 32 and 33 are located beneath the conveyor 10. The ramp 31 may, for example, be approximately 7.5 cm long and may include sixteen photodiodes 32 at 5 mm spacings. A light emitting diode (LED) 34' is mounted approximately 50 cm above the conveyor 10, over the centre of ramp 31.The LED 34' is supplied from, and all the photodiodes 32,33 are electrically connected to an electronic unit 40 which may be formed by a collection of simple electronic circuits or by a microcomputer programmed in a manner known to determine, on the basis of signals received from the measuring device 30, the position of the retracted corner H relative a reference or zero line L, and to generate a command signal for a position adjusting means to displace the saw blade 12 in the direction S to a position which is the same distance from the reference line L. The position adjusting means is formed by the above-mentioned double working, pressure fluid driven cylinder-piston-assembly 16 which is connected to a pressure fluid source (not shown) via conduits 17a and a distributor valve 17 which is controlled by the electronic unit 40 in the manner already mentioned.In practice, several cylinder piston assemblies, one piled upon the other, are preferably used. For example, four assemblies, having motion extents 0.5, 1, 2 and 4 cm respectively, may be provided to permit positioning of the saw blade 12 in 0.5 cm steps within a zone 0 to 7.5 cm. A stationary, straight stop 19 is mounted adjacent the conveyor 10. The side of the stop 19 which faces the conveyor 10 extends parallel to the feed direction R and is located exactly on the reference line L. At least one end position adjusting roller 18 is in known manner mounted beneath the conveyor 10 and engages each board 20, 21 passing above it in order to move it in the direction Tuntil the board 20, 21 abuts the end stop 19.

Another measuring ramp 31" which is shown by interrupted lines may replace ramp 31 and has the same fundamental construction as the ramp 31, although the elements 31,32 and 34' are not shown for the sake of clarity. The ramp 31" is however considerably longer than ramp 31 and its function will be discussed later. The stop 19 is preferably retractable so that an operator may in the conventional manner described above handle those boards 20, 21 where due to defects a greater portion has to be cut off (the engagement of the roller 18 with such a board being interrupted). Alternatively, in the embodiment of Figure 2, to be described below, the operator is positioned in a space provided for the purpose between, in feed direction, a settable stop 19' which does not need to be retractable and the saw blade 12 (stationary in this embodiment).

The arrangement of Figure 1 operates as follows: The boards 20, 21 etc, are conveyed on the conveyor 10 in the direction R generally in an arbitrary longitudinal position (i.e. in view of distance n' between the retracted corner H and a lateral margin of conveyor 10 which may coincide with the said reference or zero line L), but thanks to the carrier elements 11, always at right angles to the feed direction R. Before a board 20, 21 reaches the measuring device 30, it is displaced in the direction T by one or several rollers 18 engaging the board from beneath until the board hits the stationary straight stop 19 with its projecting corner G (so called "end - alignment"). All boards 20, 21 are thus fed past the measuring ramp 31 in a position where their projecting corners G lie on the reference or zero line L. The distance of the retracted corner Hfrom the reference line L is measured by the measuring device 30 in a manner which will be explained later. This distance is equal to the distance by which the saw blade 12, or more precisely, the saw plane U thereof, must be spaced from the reference line L in order that the cross-cut at the root end passes through the retracted corner H, i.e. is located in plane Z. A corresponding command signal for the means 16,17 is generated in the electronic unit 40 and the necessary displacement of the motor 13 on the guides 1 5a, 1 sub, or, alternatively, only of the saw blade 12, is effected.In the example shown, the displacement is equal to the distance n between the corners H and G (because it has been supposed that the initial position of the saw blade 12 was on the reference or zero line L). Thus, in Figure 1, the saw blade 12 is shown in a position which, as a rule, it will occupy only after the board 21 has passed the measuring device 30.

Figure 2 illustrates part of a modified embodiment of the device of the invention in which the motor 13 and the saw blade 12 are mounted so as to remain stationary. The measuring device 30' is principally the same as in the example illustrated in Figure 1, but comprises a plurality of LEDs 34 and an additional LED 33' on the ramp 31' and a single photodiode 32' above the ramp 31". The measurement is made in the same manner as in Figure 1, after the projecting corner G of the board 21 has been pressed against the stationary stop 19 due to the action of at least one roller (not shown), similar to the roller 18.

However, behind the stationary stop 19 there is a short displaceable stop 19' which is fixed to the piston rod 16'a of the double working, pressure fluid driven cylinder piston assembly 16'. The command signal from the electronic unit 40 controls the assembly 16' via the distributorvalve means 17' so that the stop 19' is set to the distance n, determined in the measuring device 30', relative to the stationary saw blade 12. The measuring ramp 31' is provided with a set of light emitting diodes 34, and an additional diode 33' in an advanced position, as already mentioned. A photodiode 32' is mounted above the conveyor 10. The dimensions and spacings thereof may be the same as stated in connectin with Figure 1.

An alternative location 31 'a of the measuring ramp 31', to be explained in more detail later, is shown in Figure 2. It will, however, be understood that the embodiment with a displaceable saw blade as shown in Figure 1 can also have an inclined measuring ramp which may or may not be provided with light emitting diodes, and the embodiment of Figure 2 can alternatively have a measuring ramp (extending at right angles or obliquely) with photodiodes or photocells.

A third and a fourth embodiment of the device of the invention correspond to Figure 1 and Figure 2 respectively with the distinction that the stationary stop 19, and thereby also the operational step of "end alignment", is quite eliminated. The boards 20, 21 are conveyed on the conveyor 10 in their arbitrary transverse positions (see board 20 in Figure 1) as far as to the measuring device 30. The measuring ramp must in this case be considerably longer than only to cover the marginal region of the conveyor 10, and must cover, for example, one third of the entire breath (transverse dimension) of the conveyor, as shown in ramp 31" in Figure 1.The distance n' between the retracted corner G and the - in this case quite hypothetical - reference line L is determined in the measuring device 30 and in the electronic unit 40 in the same manner as before, and either saw blade 12 is displaced to the same distance from the reference line (in the embodiment in analogy to Figure 1), or, preferably, the shorter stop 19' is displaced so that the plane Z coincides with the plane of saw blade 12 (in the embodiment in analogy to Figure 2). It will be noted that in the embodiment according to Figure 2, and in the embodiment just described which is analogous thereto, a driven "end aiignment" roller 18 is provided beneath the operational area ofthe displaceable stop 19' and displaces the board so that it abuts said stop 19'.

Any arbitrary, suitably contact-free measuring device suitable for the purpose can, in principle, be used. Preferably, as already stated, either a set of photodiodes (or photoelectric cells) in combination with a LED, or a set of LEDs in combination with a photodiode or a photoelectric cell are used, the individual elements being turned on and off, or, more exactly, read-off (as to illuminated state or not) by the electronic unit 40. In this unit 40 the position ofthe sawing cut (plane Z) is determined and positioning of the saw blade 12 or of the short stop 19' is effected. A suitable electronic unit for this purpose may be formed, as already stated, by a plurality of simple electronic circuits, or by a microcomputer, such as INTEL 8085.

A measuring device with a single LED 34' and a plurality of photodiodes or photoelectric cells 32 operates according to Figure 3 as follows: The LED 34' (Figure 1) above the measuring ramp 31 emits light continuously. When the additional upstream photodiode 33 is obscured by a conveyed board 20, reading-off of the other photodiodes 32 starts. These photodiodes 32 may be divided into two groups, namely a group IA which is never illuminated, and a group IlAwhich is illuminated at least during a part of the time when the board 20 passes by. The boundary between these two groups indicates the position of the retracted corner H. When the position of the measuring ramp 31 relative to the reference line L is known, also the position of this corner relative to the reference line is thereby established.

Reading-off is stopped either when the additional photodiode 33 again becomes illuminated, or, in order to eliminate the influence of the short distance y between the diode 33 and the line of diodes 32 (this distance can in practice be made considerably smaller than that shown in the drawing for clearness), when all diodes 32, i.e. both groups IA and IIA, are illuminated at the same time.

It will be understood that no change in this principle of measurement occurs when a measuring clamp 31" (Figure 1) of greater length than ramp 31 of Figure 3 is used.

A measuring device with a single photodiode or photoelectric cell, as shown in Figure 2, operates according to Figure 4 in the following manner. The LEDs 34 on the measuring ramp 31' are turned on and off sequentially, i.e. one after the other during a scan. The photodiode 32' (Figure 1) is read off each time a LED 34 is turned on. Illumination of this photodiode 32' indicates that at this moment the board 20 does not obscure the path of rays between the LED 34 which is turned on and the photodiode 32'. When the photodiode 32' does not receive any light, it means that the LED 34, which is turned on, is obscured by the board 20.

The scanning starts when the additional LED 33', which emits light continuously, is screened thereby indicating that a board 20 is arriving. All the LEDs 34 are then scanned until the additional LED 33' is no longer screened, whereupon the scanning is stopped. Alternatively, stopping may be triggered by all LEDs becoming uncovered, i.e. group IB which, as long as a given board 20 passes by, can never transmit light as far as to the photodiode 32', as well as group IIB which, at least during a part of the time when said board is passing by, can do so.

One scanning movement is executed so fast (taking approximately 10 MS or less) that the position of the board 20 in the direction of the longitudinal axisx is determined at approximately each centimetre of its width in the direction R when the conveying speed is about 1 meter per second.

The measuring ramp 31,31' is located as close as possible beneath the board 20 which is passing by in order to minimize the parallax error depending on the ratio between the emitter-transmitter distance and the length of the ramp 31,31'. With the parameters given above, i.e. sixteen elements spaced 5 mm apart on the ramp 31,31', and the element 32' or 34' located 50 cm above the ramp, the said error should be negligible.It may, however, be totally eliminated, if as shown in Figure 5 a measuring device 30" comprises two parallel measuring ramps 31"a and 31"b of which one is located close beneath the board 20 and the other one just high enough above the conveyor 10 as to allow the thickest measured object occuring in practice to pass by, e.g. 15 cm above the cross-conveyor 10 on which the boards 20, 21 are conveyed. Light guides 36, 36b e.g. sixteen such light guides, are anchored with their terminal portions in each ramp 31"a, 31"6 at 5 mm spacings.Each pair of light guides, 36a, 36b, the terminal portions of which are located opposite one another in respective measuring ramps 31"a, 31"b, is connected to a separate photoelectronic switch, as is shown for the guides 36a' and 36b' which are connected to a switch 37. Each photo-electronic switch 37 comprises a light source function and a photoelectric cell function. In Figure 5 it is supposed that all light guides 36a are connected to the light source in the respective switch 37 and all light guides 36b to the photocell therein. The single upstream indicator element is defined by a further pair of light guide ends in a corresponding upstream position.Radiation from a first group IC of light guides 36a is screened by the board 20 passing by, while radiation from a second group IIC can reach the light guides 36b without being impeded. In a similar manner to the measuring devices described above, the position of the retracted corner of the board 20 is determined as the boundary between the light guides which never become activated when the board 20 passes, and those which become activated at least during a part of that time. Also in a similar manner to the two other above-described measuring devices, a pair of light guides (not shown) is arranged somewhat upstream in order to start the reading-off process. Preferably, neighbouring electronic switches are trimmed to operate at different wave lengths, whereby special logical controls or other measures to prevent "crosstalk" may be totally dispensed with.A suitable electronic switch is, for example, the switch distributed in commerce under the name "Hemomatik", type FM-30-500-3L SNO.

The resolving power of the measuring devices is determined by the spacing of the indicator elements on the measuring ramp. If desired, the resolving power can be increased by arranging the ramp at an anlge 0 < a < 90" relative the feed direction R, as in measuring ramp 31 'a shown by interrupted lines in Figure 2, and the electronic unit 40 is programmed for conversion to distances in the direction of longitudinal axisx. The measuring ramps 31,31', 31", 31 'a, 31"b are always turned towards one of the plane faces a, b of the measured board 20, 21, and more specifically towards the lower plane face b in the example shown.The single elements 32', 34', or the second, parallel measuring ramp 31"a, are turned towards the opposite plane face of the board, i.e. the face a in the illustrated examples.

The electronic unit 40 operates in principle in the same way in all embodiments. Taking as an example the embodiment of the invention described in connection with Figures 2 and 4, the operational block diagram of the electronic unit 40 may be as shown in Figure 6. As soon as the presence of a new piece of timber 20 in the measuring zone has been indicated by the advance LED" 33', the LEDs 34 on the ramp 31' are activated and deactivated in subsequent scans. If in a particular scan more LEDs 34 are visible to the photodiode 32' than during the previous scan (which only can happen when terminal edge e is oblique).

an end cut function, which has been set at zero when scanning started, is augmented as corresponds to the number of newly visible LEDs 34. When the indication comes that the piece of timber 20 has left the measuring zone, said function is read-off and a corresponding command signal for valve means 17, 17I is generated, said function is reset at zero and unit 40 is ready to await a new piece of timber.

Further alternatives are possible within the scope of the invention. An additional indicator element (photodiode, LED, pair of light guides) may for example, be located on the measuring ramps downstream of the assembly of elements in order to generate a stop signal for the measuring operations.

The described additional element located downstream may also be used for a logical functionai check. Furthermore other electromagnetic radiation, such as infrared light, can be used instead of visible light in order, in a manner known per se, to avoid disturbances caused by environmental illumination.

The stationary stop 19 can also be located at some other selected spacing than zero from the reference line L.

Claims (14)

1. A method of cross-cutting the root end part of elongate pieces of timber, such as boards and planks, each having a top end and a root end and being, in an arbitrary longitudinal position, conveyed in transverse direction past a stationary, elongate measuring device, extending transversely or obliquely to the feed direction of the pieces of timber, and onwards to a cross-cutting saw blade, and, at some stage during their progress towards the saw blade, said pieces of timber each being displaced in their longitudinal direction until their respective root ends bear against a stop means, characterised in that with each piece of timber having at its root end a sloping edge limited by a retracted corner and a projecting corner, the distance in the longitudinal direction between the projecting and the retracted corner of each piece of timber is measured by the measuring device which generates signals which are fed into an electronic unit where a command signal, corresponding thereto, is generated and is fed to a displacement means to control said displacement means to displace in the longitudinal direction of each piece of timber either at least a part of said stop means, or the cross-cutting saw blade, until the retracted corner of each piece of timber lies in the cross-cutting plane of the cross-cutting saw blade, whereby waste at the cross-cut on the root end is minimized.

2. A method as claimed in claim 1,wherein each piece of timber, before it reaches the measuring device, is displaced longitudinally in the direction of its root end until its projecting corner hits a stationary stop means, which is rectilinear, elongate and extends parallel to the transverse feed direction of the pieces of timber, each piece of timber being subsequently conveyed past the measuring device with its projecting corner sliding along said stationary stop means.

3. A method as claimed in claim 1 wherein each piece of timber, after it has passed the measuring device, is displaced longitudinally in the direction of its root end until its projecting corner hits the stop means, which is rectilinear, elongate and extends parallel to the transverse feed direction of the pieces of timbers, each piece of timber being subsequently conveyed towards the cross-cutting saw blade with its projecting corner sliding along said stop means.

4. A device for cross-cutting the root end part of elongate pieces of timber, such as boards and planks, each having a top end and a root end, said device comprising a cross-conveyor which serves to convey the pieces of timber, each in an arbitrary longitudinal position, in transverse direction past a stationary, elongate measuring device extending transversely or obliquely to the feed direction of the pieces of timber, and onwards to a cross-cutting saw blade, means to longitudinally displace the pieces of timber on the conveyor and thereafter cause the root end of each piece to be continuously pressed against stop means, extending parallel to the feed direction, characterised in that to enable cutting off of the root end part of said pieces of timber, each piece having at its root end a sloping edge limited by a retracted corner and a projecting corner, the measuring device is arranged to measure the distance in the longitudinal direction of each piece of timber between the projecting and the retracted corner and is electrically connected to an electronic unit adapted to receive measuring signals from said meaning device and to generate corresponding command signals, powerdriven displacement means controllable by said command signals being provided to displace, in the longitudinal direction of each piece of timber, either at least a part of the stop means, or the cross-cutting saw blade, until the retracted corner of each piece of timber lies in the cross-cutting plane of the crosscutting saw blade.

5. A device as claimed in claim 4 wherein the stop means is elongate and rectilinear and at least part of said stop means is located upstream of the measuring device and is stationary in the direction at right angles to the feed direction.

6. A device as claimed in claim 5 wherein a further portion of the stop means is arranged between said stationary stop means and the saw blade, and is displaceable by said displacement means at right angles to the feed direction.

7. A device as claimed in claim 4,5 or 6, wherein the measuring device comprises at least one rectilinear assembly of a plurality of measuring elements located on one side of the pieces of timber, and at least one co-operating element on the opposite side thereof.

8. A device as claimed in claim 7, wherein an additional element is provided upstream of said assembly to generate a start signal, or a start signal and a stop signal, for each measuring operation.

9. A device as claimed in claim 7, wherein a respective additional element is provided upstream and downstream of said assembly to generate a respective start and stop signal for each measuring operation.

10. A device as claimed in claim 7,8 or 9, wherein the element or elements on the one side of the pieces of timber are in the form of photodiodes, and on the other side in the form of light emitting diodes, or vice versa.

11. A device as claimed in any one of claims 7 to 10, wherein the assembly is located close to the pieces of timber passing by and the co-operating element or elements is/or are located at a distance of the order of 0.5 m from the pieces of timber.

12. A device as claimed in claim 7,8 or 9, wherein the measuring device comprises two parallel measuring ramps located on opposite sides of the pieces of timber passing by, a plurality of pairs of light guides being arranged with their respective terminal portions opposing each other in the respective measuring ramps, each pair of light guides being connected to a separate photo-electronic switch.

13. A method of cross-cutting the root end part of elongate pieces of timber substantially as hereinbefore described.

14. A device for cross-cutting the root end part of elongate pieces of timber substantially as hereinbefore described with reference to and as illustrated in Figures 1 and 3, or in Figures 2 and 4 of the accompanying drawings.