How To Draw Loci For Crank Mechanism

Definition

A locus (plural foci) is tha path traced out by a point which moves under given definite conditions

You may not have been aware ot it but you have met loo meny times before. One of the most common loci is that of a point which moves so that its distance from another fixed point remains constant, this produces a circle Another locus that you know is that ot a point which moves so that its distance from a line remains constant: this produces parallel lines.

Problems on loci can take several different forms. One important practical application is finding the path traced out by points on mechanisms This may be done simply to see If there is sufficient cleaiance around a mechanism or. with further knowledge beyond the scope of this book, to determine the velocity and hence the forces acting upon a component

There are very few rules to learn about loci; it is mainly a subject for common sense A locus is formed by continuous movement and you have to 'stop' the movement several times and find and plot the position of the point that you are interested in. Take, for instance, the case ol the men who was too lary to put wedges under his ladder The inevitable happened and the ladder slipped. The path that the feet ot the man took is shown in Fig 9/1.

The top of the ladder slips from T to Tr The motion of the top of the ladder has been stopped at T„ T* T* etc. end. since the length of the ladder remains constant, the corresponding positions of the bottom of the ladder. B,. B;. B y etc. can be found. The positions of the ladder T,B,. T,B,. T,Betc are drawn and the position of the man's feet 1. 2. 3, etc.. are marked. The points are joined together with a smooth curve. It is interesting to note that the man hits the ground at right angles (assuming that he remains on the ladder) The resulting jar often causes serious injury and is one of the reasons for using chocks Another simple example is the locus ol the end of a

Fig 9/1

Loci Ladder Slipping

Fig 9/1

bureau door stay. Fig. 9/2. This type of stay is also often used on wardrobe doors, lis function is to allow the door to open to a certain point, and then to support the door in that position.

The stay, of course, has two ends and the locus on one end is essily found: it is en arc whose centre is the hinge. The other end of the stay is allowed to slide through the pin but it is not allowed to move off it. As the end of the stay moves along the arc. its movement is stopped several times and the position of the other end of the stay is marked. These points are joined together with a smooth curve. Obviously the designer of such a bureau would have to plot this locus before deciding the depth of the bureau.

Loci of mechanisms

The bureau door stay is a very simple mechanism. We now look at some of the loci that can be found on the moving parts of some machines.

Definitions

Velocity is speed in a given direction. It is a term usuelly reserved for inanimate objects; we talk about the muzzle velocity of a rifle or the escape velocity of a space probe When we use the word speed we refer only to the rate of motion. When we use the word velocity we refer to the rate of motion and the direction of the motion.

Linear velocity is velocity elong a straight line (a linear graph is a straight line).

Angular velocity is movement through a certain angle in a certain time. It makes no allowance for distance travel • led. If, as in Fig. 9/3, a point P moves through 60" in 1 second, its angular velocity is exactly the same as that of 0. providing that Q also travels through 6CP in 1 second. The velocity, as distinct from the angular velocity, will be much greater of course.

Constant velocity, linear or angular, is movement without accelaration or deceleration

The piston/connecting rod/crank mechanism is very widely used, pnncipelly because of its application in internal combustion engines The piston travels in a straight line: the crank rotates The connecting rod.

straight line: the crank rotates The connecting rod.

How Draw Crank Mechanism

be 'stopped' several times and the positions of the centre of the connecting rod found. As with most machines that have cranks, the best policy a to plot the position of the crank in twelve equally spaced positions. This is easily achieved with a 60" set square The piston must always lie on the centre line and. of course, the connecting rod cannot change its length. It is therefore a simple matter to plot the position of the connecting rod for the twelve positions of the crank This is best done with compasses or dividers. The mid-point of the connecting rod can then be marked with dividers and the points joined together with a smooth curve.

The direction of rotation of the crank is usually given m problems of this nature. It may make no difference to plotting any of the loci but it could make a tremendous difference to the functioning of the real machine: what good is a car that does 120 km/h backwards and 10 km/h forwards 7

Trammels

A trammel can consist of a piece of paper or a piece of card or even the edge of a set square It must have a straight edge and you must be able to mark It with a pencil. A trammel enables you to plot a locus more quickty than the method shown above However, if you are intending to sit the G.C.E. or C.S.E. examination check that the syllabus allows you to use trammels.

Fig. 9/5 shows a crank/rod/slider mechanism where a point | along the rod has been plotted for one revolution of the crank. The length of the rod. and the point, are marked on a piece of paper One end of the rod is constrained to travel around the crank circle and the other slides up and down the centre line of the slider. Move the trammel so that one end is always on the circle whilst the other end is always on the slider centre line, marking the required point as many times as necessary. Join the points with a smooth curve.

Geometric Locus

On mechanism» that ere more complicated, it is sometimes necessary to plot one locus to obtain another Fig. 9/6 shows a mechanism which consists of two cranks. 0,A and 0,B. and two links. AB and CD. It is required to plot the locus of P. a point on the lower end of the hnk CO

Before we can plot any positions of the link CD. end hence P. we must know the position of C at any given moment. This can only be done by plotting the locus of C. ignoring the link CD. Once this has been done, we can find the position of CD at any given moment, and hence the locus of point P.

Geometrical Loci

No construction lines are shown in Fig. 9/6 since they would only make the drawing even more confusing I The locus of P could have been found by stopping' one of the cranks in twelve different places and finding the twelve new positions of the link AB This, in turn, would enable you to find twelve positions for C. end then twelve positions of the rod CD. Finally this would lead to the twelve required positions of P. Alternatively, the locus of C could have been plotted with a trammel which had the length of the link AB. and the position of C marked on it. Another trammel, with the length of the rod CD and the position of P marked on it would have given the locus of P.

Some Other Probiema in Loci A locus is defined as the path traced out by a point which moves under given definite conditions. Three examples of loci are shown below where a point moves relative to another point or to lines

To plot the locua of ■ point P which moves so thst Its distance from a point S and a line X-Y ia always the aeme (fig. 9/7)

The point S is 20 mm from the line X-Y.

The first point to plot is the one that lies between S and the line. Since S is 20 mm from the line, and P is equidistant from both, this first point is 10 mm from both.

If we now let the point P be 20 mm from S. It will lie somewhere on the circumference of a circle, centre S. radius 20 mm. Since the point is equidistant from the line, it must also lie on a line drawn parallel to X-Y and 20 mm away. The second point then, is the intersection of the 20 mm radius arc and the parallel line.

The third point is et the intersection of an arc, radius 30 mm and centre S. and a line drawn parallel to X-Y and 30 mm away.

The fourth point is 40 mm from both the line end the point S. This may be continued for as long as is required.

The curve produced is a parabola.

DIMENSIONS IN

To plot the locu« of a point P which moves so that its distance from two fixad point* R and S. 50 mm apart, is always in the ratio 2:1 respectively (Fig 9/8)

As in the previous example, the first point to plot is the one that lies between R and S- Since It is twice as far away from R as it is from S. this is done by proportional division of the line RS.

If wo now let P be 40 mm from R it must be 20 mm from S. Thus, the second position of P is at the intersection of an arc. centre R. radius 40 mm and another arc. centre S and radius 20 mm.

The third position of P is the intersection of arcs, radii 60 mm and 25 mm. centres R and S respectively.

This is continued for es long as necessary. In this case, at a point 100 mm from R and 50 mm from S, the locus meets itself to form a circle.

How Draw Loci

To plot the locus of a point P which moves so that its distance from the circumference of two circles, centres 0, and 0, and radii 20 mm and 15 mm respectively, is alwaye in the ratio 2:3 respectively (Fig. 9/9)

As with the two previous exemples. the first point to plot is the one that lies between the two circles. Thus, divide the spece between the two circumferences in the ratio 3:2 by proportional division.

If we now let P be 10 mm from the circumference of the circle, Centre O,. it will lie somewhere on a circle, centre 0,. and radius 30 mm If it is 10 mm from the circumference of the circle, centre 0,, it will be 15 mm from the circumference of the circle, centre 0,. since the ratio of the distances of P from the circumferences of the circles is 3:2. Thus, the second position of P is the intersection of two arcs, radii 30 mm and 30 mm. centres O, and 0a.

How Draw Crank Mechanism

Exercises 9

(All questions originally set in Imperial units) . Fig. 1 shows e door stay as used on a wardrobe door. The door is shown in the fully open position Draw. luH tit», the locus of end A of the stay as the door closes to the fully closed position The stay need only be shown diagrammatically as in Fig. 1 A. Wett Midlands Examinations Board |--15-0-J

DIMENSIONS IN *« 2 Fig. 2 shows a sketch of the working pans, sod the working parts represented by lines, of a moped engine. Using the line diagram only, and drawing in single lines only, plot, full sue. the locus of the point P for one full turn of the crank BC.

Do not attempt to draw the detail shown in the sketch

Show all construction.

The trammel method must not be used.

East Anghan Examinations Board

3. In Fig 3 the crank C rotates in a clockwise direction The rod P8 is connected to the crank at B and slides through the pivot D.

Plot, to a scale 1 { full site, the locus of P for one revolution of the crank.

South ■ East Regional Examinations Board

4. In Fig. 4 the stay BHA is pin-pointed at H and is free to rotate about the fixed point B Plot the locus of P as end A moves from A to A'. North Western Secondary School Examinations Board

DIMENSIONS IN i»m 5 In Fig. 5. rollers 1 and 2 are attached to the angled rod. Roller 1 slides along slot AB while roller 2 slides along CD end back.

Draw, fuU site, the locus of P. the end of the rod. for the complete movement of roller 1 from A to B South East Regional Examinations Board

6 As an expenment a very low gear has been fitted to a bicycle. This gear allows the bicycle to move forward 50 mm for every 15 dog roes rotation of the crank and pedal. These details are shown in Fig. 6.

(a) Oraw. half full size, the crartk and pedal in position as it rotates for every 50 mm forward motion of the bicycle up to a distance of 600 mm. The first forward position has been shown on the drawing

(b) Draw a smooth freehand curve through the positions of the pedal which you have plotted

(c) From your drawing find the angle of the crank OA to the horizontal when the bicycle has moved forward 255 mm.

Metropolitan Regional Examinations Board ^fCOAL

PosiroN or rcoA«. AND CAAN« AFT»« Ö'O» ROTTAT*

TORWMCO MCT«0»i C.eiCYCUi

7. Fig. 7 is a line diagram of a slotted link and crank of • shaping machine mechanism. The link AC is attached to a fixed point A about which it is free to move about the fixed point on the disc. The di9C rotates about centre 0. Attached to C and free to move easily about the points C and 0 is the link CO. D is also free to slide along OE.

When the disc rotates in the direction of the arrow, plot the locus ol C. the locus of P on the link CO. and clearly show the full travel of B on AC. Southern Universities'Joint Board

8. In Fig. 8, MP and NP are rods hinged at P. and A and 0 are guides through which MP and NP are allowed to move. D is allowed to move along BC. but rod NP is always perpendicular to BC. The guide A is allowed to rotate about its fixed point. Draw the locus of P above AB for all positions and when P is always equidistant from A and BC. This locus is part of a recognised curve. Name the curve and the parts used in its construction Southern Universities' Joint Board

9. In the mechanism shown in Fig 9. OA rotates about 0. PC is pivoted at P, and OB is pivoted at 0 BCDE is a rigid hnk. OA - PC - CD - DE - 25 mm. BC — 37.5 mm. QB - 50 mm and AD — 75 mm. Plot the complete locus of E.

Oxford and Cambridge Schools Examinations Board

OIMENSIONS iH mm

Fig 9

OIMENSIONS iH mm

Fig 9

10. A rod AB 70 mm long rotates at a uniform rate about end A Plot the path of a slider S, initially coincident with A. which slides along the rod. at a uniform rate, from A to B and back to A during one complete revolution of the rod

Jornt Matriculation Board

11. With a permanent base of 100 mm. draw the locus of the vertices of all the triangles with a constant perimeter ol 225 mm.

Oxford and Cambridge Schools Examination Board

12. Three circles lie in a plane in the positions shown in Fig. 10. Draw the givon figure and plot the locus of a point which moves so that it is always equidistant from the circumferences of circles A and B Plot also the locus of a point which moves in like manner between circles A and C.

Finally draw a circle whose circumference touches the circles A. B and C and measure and state its diameter

Cambridge Local Examinations Board

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    3 years ago
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    3 years ago
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    3 years ago
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    3 years ago
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    3 years ago
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    3 years ago
  • Erik
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    3 years ago
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    3 years ago
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    3 years ago
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    3 years ago
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    3 years ago
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    3 years ago
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    3 years ago
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    3 years ago
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    3 years ago
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    How to construct the locus of a point for a complete revolution in a crank mechanism?
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    3 years ago
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    3 years ago
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    What is the use of locus in Engineering Graphics?
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    3 years ago
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    3 years ago
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    3 years ago
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    What the function of loci in mechanism?
    3 years ago
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    How to draw loci of point in a crank slider?
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    How to draw locus on a point in mechnics?
    3 years ago
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    How to draw locus on a point in mechanics?
    3 years ago
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    3 years ago
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    How to draw a loci human?
    3 years ago
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    3 years ago
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    3 years ago
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    3 years ago
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    3 years ago
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    How to draw round disc engineerers drawing?
    3 years ago
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    3 years ago
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    What are definition of mechanism in technical drawing?
    3 years ago
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    How to draw piston with a connecting rod in auto cad easy procedure?
    3 years ago
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    How to drawing star at slideing mechanism?
    3 years ago
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    How to construct locus of a pointTechnical drawing?
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    How to draw reverse circle in mecha drawing?
    3 years ago
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    How to draw locus of a line rotating anticlockwise?
    3 years ago
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    How to draw the locus deecribed by crank and shaft?
    3 years ago
  • liya
    How to apply loci of points in technical drawing?
    2 years ago
  • MEZAN
    How to plot conrod movement graph?
    2 years ago
  • Joan
    How to draw locus made by piston?
    2 years ago
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    What is locust in technical drawing?
    2 years ago
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    How to draw locus point on a connecting rods?
    2 years ago
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    What does maximum movement of a rod on both axis implies technical drawing?
    2 years ago
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    How to draw the locus method problems in caed?
    2 years ago
  • eddie
    How to plot locus on revolving cranks?
    2 years ago
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    How to plot the locus for one revolution og cranks?
    2 years ago
  • ROBINIA
    How to draw pinion locus?
    2 years ago
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    How todraw. angled CAM Loci?
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    How to plot loci on link mechanism?
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    How to guard a rotating mechanism in loci?
    2 years ago
  • charley
    How to draw a loci (cam)?
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    How to construct loci engineering graphics?
    2 years ago
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    How to draw mechanisms emgineering?
    2 years ago
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    How to plot loci of a point on a different link mechanism?
    2 years ago
  • Max
    How to draw a locus that consists of two cranks?
    2 years ago
  • Daria
    How to draw locus in details?
    2 years ago
  • mustafa awet
    What does a stoke mean them ut comes to loci cam?
    2 years ago
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    How to draw a locus in a triangle which has been given a lengh from it?
    2 years ago
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    How to work with Loci grade 12?
    2 years ago
  • Ursula
    How to construct a links mechanism?
    2 years ago
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    How to draw the locus of a point on a connecting rod joined to a crank?
    2 years ago
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    2 years ago
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    How to draw a loci mechanical?
    2 years ago
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    What are the procedure in construting a link mechism?
    2 years ago
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    How to draw a locus between 2 circles?
    2 years ago
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    How to draw the locus of a moving point?
    2 years ago
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    How to bisect locus of mechanism with crank?
    2 years ago
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    How to contruct link mechanism?
    2 years ago
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    How to construct a link mechsnism?
    2 years ago
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    How to draw a four link slide mechanism pdf?
    2 years ago
  • Claudio
    How to plot a lucci on different link mechanism?
    2 years ago
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    How to draw a link mechanics?
    2 years ago
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    How to draw locus to a point in engineering graphics?
    2 years ago
  • christin
    How to construct a for the locus of a linkage mechanism?
    2 years ago
  • michael
    How to draw locus in engineering drawing?
    2 years ago
  • courtney
    How to construct locus of mechanisim?
    2 years ago
  • Ali
    How to draw loci for link mechanism showing clear steps?
    2 years ago
  • katharina theiss
    How to construct a loci link mechanism?
    2 years ago
  • S
    What is mechanism in technical drowing?
    2 years ago
  • SAMIRA
    How to draw Slider and Crank mechanism step by step?
    2 years ago
  • donald
    How to draw loci mechanisms grade 12?
    2 years ago
  • LOUIE
    What is a locuse in technical drawingi?
    2 years ago
  • basso
    What is mechanism in technical drawingi?
    2 years ago
  • ALMA
    What is locus of a point created in crank shaft?
    2 years ago
  • viljo
    How to draw a loci of point given a ratio?
    2 years ago
  • romola
    How to draw crankshaft using technical drawing?
    2 years ago
  • Dawit
    What is the meaning of a locus in geometric construction.?
    2 years ago
  • donna
    How to construct single slider mechanism pdf?
    2 years ago
  • mhairi
    How to draw a crank BC rotates about a fixed centre/?
    2 years ago
  • jessica wood
    How to draw locus of wheel revolving in opposite directions?
    2 years ago
  • judith
    How to get the position of some points on a slider crank mechanism?
    2 years ago
  • hope
    How to draw full size of the locus of point p when the crank make one revolution?
    2 years ago
  • colby
    How to draw alocus of acrank shaft?
    2 years ago
  • SESUNA
    How to plot a locus two crancks connected to a rod?
    2 years ago
  • Futsum
    How to solve loci problem on technical drawing?
    2 years ago
  • Kiara
    How to draw the locus of a link mechanism that is on a given rack?
    2 years ago
  • Hamilcar
    How to draw alocus of a grankshaft pdf?
    2 years ago
  • mustafa michael
    How to draw a locus in a diagram of a simple machine?
    2 years ago
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    How to construct a simple link mechanism with construction method?
    2 years ago
  • HENDING
    What is locus and its application technical drawing?
    2 years ago
  • eleonora
    How to construct a crank in anticlockwise?
    2 years ago
  • mustafa
    How yo construct loci to points and mechanism?
    2 years ago
  • sebhat
    How to draw simple mechanism of piston?
    2 years ago
  • Juliane
    How to construct a slider crank mechanism?
    2 years ago
  • amina
    How to construct the locus of one revolution of two crank in opposite direction?
    2 years ago
  • remo
    How to construct the locus of crank rotating clockwise at constant speed and one revolution?
    2 years ago
  • PATRICE
    How to draw complete loci for Watt's straight line motion?
    2 years ago
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    How to plot a locus of a point in technical drawing?
    2 years ago
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    How do i construct mechnism in technical drawing?
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    How do i construct a crack mechnism in technical drawing?
    2 years ago
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    How to draw simple slider crank mechanism pdf?
    2 years ago
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    How to construct locus of a point on engineering drawing?
    2 years ago
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    How to locate a loci on mechanical drawing?
    2 years ago
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    How to draw a locus eclipse of distance from two unequal diameter circles in technical drawing?
    2 years ago
  • ville-veik p
    How to construct a locus in engine drawings?
    2 years ago
  • Mehari
    How to reproduce link mechanism in engineering drawing?
    1 year ago
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    How to draw loci for crank mechanism when it reaches B?
    1 year ago
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    How to trace a locus of a point in engineering drawing?
    1 year ago
  • FREDEGAR HAYWARD
    How to drae simple link mechanism?
    1 year ago
  • arto
    How to plot locus of points on a crank of a turning while?
    1 year ago
  • EVIE
    What Is The Procedure Governing The Drowing A Linkage Mechanism?
    1 year ago
  • christina
    HOW TO CONSTRUCT THE LOCUS OF A LINK MECHNISM?
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    How to draw loci mechanism of a engine piston?
    1 year ago
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    HOW TO PLOT LOCUS OF MECHANISMS U TUBE?
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    How to drawn crank mechanism?
    1 year ago
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    How to do locus construction in engineering?
    1 year ago
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    How to draw the curve of a crunk mechanism?
    1 year ago
  • magnus
    How to draw a loci mechanic?
    1 year ago
  • yrj
    How to draw the cloxkwise and anticlockwise of a crank mechanism?
    1 year ago
  • lillie
    How to constuct a linking mechnism?
    1 year ago
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    How to plot locus of links?
    1 year ago
  • bandobras
    How to draw locus of folding doors?
    1 year ago
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    How to draw elliptical from crank?
    1 year ago
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    How to plot locus of a slider crank?
    1 year ago
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    How to construct linkage mechanism in engineering drawings?
    1 year ago
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    How to construct the loci of point on link mechanism?
    1 year ago
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    How to draw aLocus of a circle?
    1 year ago
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    How to draw the loxcus of a point?
    1 year ago
  • Lucas
    How To Draw Locus Of A Point On The Connection Of A Simple Machine?
    1 year ago
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    How to draw a Loci Helix fast methods on EGD?
    1 year ago
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    How to draw a crank mechanism in engr drawing?
    1 year ago
  • igino
    How can you trace a locus of simple link mechanism?
    1 year ago
  • HEATHER
    How is link mechanism drawn?
    1 year ago
  • Taneli
    How to draw locus of apoint?
    1 year ago
  • ishbel
    How 2 do a loci step by step egd instructions?
    1 year ago
  • Tony Paarma
    How to draw an machanism in egd grade 12?
    1 year ago
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    How to do a slotted and link mechanism egd?
    1 year ago
  • Felix Mahler
    What is the method of finding the locus of a point on a mechanism?
    1 year ago
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    How to draw 15 degree in techincal drawing?
    1 year ago
  • rita
    How to draw the loci of moving and sliding mechanism?
    11 months ago
  • huriyyah
    How to construct the locus of an engines connecting rod?
    11 months ago
  • mebrat saare
    How to draw simple mechanisms in technical drawing?
    11 months ago
  • Kenzie
    How to draw a double link mechanism loci?
    11 months ago
  • settimo
    How to take locus of simple mechanics?
    10 months ago
  • arnold
    How to draw loci of crank shaft for simple mechanics?
    10 months ago
  • lavinia
    How to find a locus of point in a cranks slider mechanis?
    9 months ago
  • Uwe
    How to construct a slidding ladder engineering drawing?
    9 months ago
  • jenson
    What is meant by the word crank as used in loci drawing?
    9 months ago
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    How to draw a simple machanism?
    9 months ago
  • fiorello
    How to construct the loci of a bureau door?
    8 months ago
  • kaari paija
    How to construct a link mechanism in one complete revolution?
    8 months ago
  • RUBY
    How to construct crank mechnism?
    7 months ago
  • jaime
    What is connecting rod in link mechanism drawing?
    6 months ago
  • Olive
    How to draw locus of a crank passing through a point?
    6 months ago
  • Davide
    How to construct the locus wen connected to a rod and shaft?
    5 months ago
  • Walter
    How to draw the locus of linked clanks?
    5 months ago
  • maire
    How to sketch a crank and rocker in autocad?
    4 months ago
  • MIKA
    How to do constructions on link mechanism engineering graphics?
    4 months ago
  • UMBERTO CREMONESI
    How to draw a licus of a point in mechanism?
    3 months ago
  • ORNELLA
    How to draw the locus of point o when the crank makes one complete revolution?
    3 months ago
  • dawn gray
    What is link mechanisim?
    2 months ago
  • matthew
    How to construct a locus of a wardrobe?
    2 months ago
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    How to plot the locus of a point p for one complete revolution of the circle?
    2 months ago
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    How to draw a loci in technical drawning?
    1 month ago
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    How to draw the locus of a point on link mechanism?
    1 month ago

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