Grade 10 power mechanics Related Drawing – Loci Notes

1. Identify and outline sub-sub-strands:
   • Definition of loci in drawing
   • Types of loci in drawing
   • Construction of different types of loci
   • Construction of loci of link mechanisms
   • Application of loci in power mechanics
2. Define a locus as used in drawing.
3. Describe types of loci used in drawing.
4. Construct different loci used in technical drawing.
5. Construct the locus of link mechanisms relevant to power mechanics.
6. Appreciate the application of loci in power mechanics.

1. Definition

A locus (plural: loci) is the path or set of all possible positions of a point that satisfies a given condition. In drawing, a locus is shown by drawing the curve or line through every possible position of that point.

Simple way to remember: "Where can the point go?" — the answer is the locus.

2. Types of Loci (common in technical drawing)

• Circle: All points at a fixed distance from a centre (e.g., path of crank pin).
• Straight line: Point constrained to move on a straight path (e.g., piston slider).
• Parallel lines / offset lines: Points at fixed distance from a line.
• Perpendicular bisector: Points equidistant from two fixed points.
• Ellipse / traced curves: Locus when sum of distances to two fixed points is constant (used in drawing practice and some link mechanisms).
• Coupler curves / complex loci: Path of a point on a moving link — can be a complex curve (important in link mechanisms).

3. Construction of Common Loci (step-by-step)

A. Circle (locus of points at fixed distance from Centre)

1. Mark the centre O.
2. Set the compass to the given radius r.
3. With the compass point on O, draw the circle. All points on the circle are at distance r from O.

B. Perpendicular bisector (locus of points equidistant from two points A and B)

1. Draw line AB.
2. From A and B, draw arcs with same radius (> half AB) so they intersect at two points.
3. Join those intersection points — the line is the perpendicular bisector; any point on it is equidistant from A and B.

C. Parallel line (locus of points at fixed distance from a given line l)

1. From several points on line l, draw perpendiculars of the given distance on the same side and mark points.
2. Join the marked points smoothly to form a line parallel to l at that distance.

D. Ellipse using string method (locus where sum of distances to two foci is constant)

1. Fix two pins at foci F1 and F2.
2. Tie a string to both pins with length = constant sum.
3. Keep the string taut with a pencil and trace — the pencil traces the ellipse.

Use compass, ruler and pins/string for practice. These basic methods build skills needed for the more complex loci of mechanisms.

4. Construction of Loci for Link Mechanisms (practical methods)

Many power-mechanics devices use rotating links and connecting rods. To find the locus of a point on a moving link we often use the graphical sampling method:

Graphical sampling method (general steps)

1. Draw the fixed parts: the frame, pivot positions and fixed centres.
2. Choose several positions for the driving link (e.g., crank) — mark angles (e.g., every 15°, 30°).
3. For each crank position, draw the connected links at their correct lengths and geometry (use compass and ruler).
4. Locate the point of interest on the moving link for every position and mark it on the drawing.
5. Join the marked points smoothly to show the locus (this gives the coupler curve or path).

Example: Crank-slider mechanism

Parts:

• Crank OA of length r that rotates about O.
• Connecting rod AB of fixed length L joined to slider sliding on a straight line.

To draw locus of A (crank pin): it is a circle of radius r about O. Locus of slider point is a straight line. Locus of a pin on the connecting rod is found by sampling positions as above — it produces a curve (not a simple circle or line).

5. Applications of Loci in Power Mechanics

• Design of mechanisms: checking the path a tool, piston, or pin will take (e.g., where a valve or a connecting-pin will reach).
• Interference checks: ensure moving parts do not collide by drawing their loci.
• Machine layout: placing guards or supports where parts will travel.
• Cam and follower design: loci guide shape design to get required motion.
• Predicting motion: helps to estimate clearances, ranges and extremes of motion before building models.

Suggested Learning Experiences (for age 15; Kenyan context)

1. Teacher demonstration: draw circles, perpendicular bisectors and parallel loci on board. Explain locus meaning with simple examples (coin on string for circle).
2. Practical exercises (individual):
   • Construct: circle (given centre and radius), perpendicular bisector of AB, parallel line at given distance from line l.
   • Use pins and string to draw an ellipse (foci given).
3. Group activity (linked to power mechanics):
   • Build a simple wooden or cardboard crank-slider or four-bar using pins and strips.
   • Trace positions of a marked point on a link as the crank is moved in steps; stick these on paper and join to show the locus.
4. Use software (optional): GeoGebra or free CAD to model a simple crank and show the locus as the crank rotates.
5. Assessment task: Given a crank of length 30 mm and connecting rod of length 90 mm, draw five positions of the mechanism (every 30°) and sketch the locus of the connecting-pin. Label extremes.

6. Classroom Tasks & Quick Assessment

1. Define locus in one sentence (LO: define locus).
2. Draw the perpendicular bisector of AB (marks: construction steps and neat line).
3. Using compass and ruler, draw the locus of a point 25 mm from centre O (a circle).
4. Practical test: Given a simple mock crank-slider, record 6 positions and plot the locus of the connecting pin. Explain what the locus tells you for machine design (clearance & range).

Marking should reward correct construction steps, accuracy of compass work and an explanation linking the drawn locus to application in a machine.

Summary

Loci are essential in technical drawing and power mechanics. Simple loci (circles, lines, bisectors) are constructed with ruler and compass. Loci of link mechanisms are found by sampling positions of the moving parts and joining points to form coupler curves. These drawings help to design safe, working machines by showing where parts will move and how they interact.

Reflection question for students

How would knowing the locus of a point help you decide where to place a safety guard around a crank in a workshop? Write two short reasons.