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3-Phase Servo AVR (AC Voltage Stabilizer) — Troubleshooting, Repair & Maintenance By Edwin Ogie • December 18, 2025 • -- AC Voltage Stabilizer — 3-phase servo control type (example from user photo) A practical, step-by-step guide to diagnose, repair and maintain 3-phase servo Automatic Voltage Regulators (AVR) / servo voltage stabilizers. Written in simple terms for technicians and maintenance teams working with generators, UPS rooms and factories. Includes videos, spare-parts list, safety checklist, troubleshooting flow and links to internal/external resources. Contents Why this matters In environments with unstable mains (frequent sags, surges or phase imbalance) a servo AVR protects sensitive equipment by continuously adjusting an autotransformer tap via a small servo motor. A well-maintained stabilizer saves equipment, reduces downtime and prevents costly damage. ...
Edwin Ogie Library: Equilibrium of Forces E-Note (Detailed)
Equilibrium of Forces – Detailed E-Note
Senior Secondary-School Physics: Forces, Moments, and Stability with detailed explanations
Page 1: What is Equilibrium?
In physics, equilibrium refers to a state where an object is not accelerating; that is, no change in its state of motion. For a body to be in equilibrium, two major conditions must be satisfied:
Translational equilibrium: the vector sum of all forces acting on the body is zero. (No net force → no acceleration.)
Rotational equilibrium: the sum of all moments (torques) about any point is zero. (No net moment → no rotation.)
Equilibrium can be static (object at rest) or dynamic (object moving with constant velocity). Even when moving steadily, if forces and moments sum to zero, the object is in equilibrium. 0
Key Points:
• Net force = 0 → ΣF = 0
• Net moment = 0 → ΣM = 0
• These must hold in two dimensions (horizontal & vertical) or more, depending on the problem.
Page 2: Free Body Diagrams & Resolving Forces
To analyze equilibrium problems, it is essential to draw a Free Body Diagram (FBD). An FBD isolates the object (or particle), showing all forces and moments acting on it, including:
Weight (W = mg), acting downward through the centre of gravity.
Normal reaction forces at supports.
Tension forces in strings, cables, ropes.
Friction (if applicable), and other external forces.
After drawing the FBD, resolve forces into components (horizontal and vertical). Use trigonometry: sine and cosine functions to find components.
Fₓ = F cos θ; Fᵧ = F sin θ
Example: A sign of weight 50 N is hung by two cables making angles 30° and 60° with the horizontal. Find the tensions in the cables so that the sign remains in equilibrium. (You would resolve each tension into vertical components summing to 50 N, and horizontal components cancelling each other.)
Page 3: Triangle & Polygon Laws of Forces
If forces act at a point (i.e., are concurrent), they are in equilibrium if they can be represented by sides of a closed polygon when placed head-to-tail.
Triangle law: for three forces in equilibrium, you can draw a triangle whose three sides represent the forces (magnitude and direction). The triangle must close.
Polygon law: extension of triangle law. For n forces acting at a point in equilibrium, when drawn head to tail in sequence, they must form a closed polygon. If not closed, not in equilibrium. 1
Visual idea: If you have forces A, B, C, with known magnitudes and directions, arranging A→B→C in sequence and connecting end of C to start of A should return to the starting point.
Lami’s Theorem applies when exactly three forces act on a point, they are coplanar, concurrent (meeting at that point), and the system is in equilibrium. Then:
F₁ / sin α = F₂ / sin β = F₃ / sin γ
Here α is the angle between forces F₂ & F₃; β between F₁ & F₃; γ between F₁ & F₂. 2
Conditions for Lami’s theorem:
Three forces only (no more, no fewer).
They must all act through the same point (concurrent).
They lie in the same plane (coplanar).
They are non-parallel (i.e. no two are acting along the same line). If two are parallel, one force may be zero or the theorem fails. 3
• Useful for finding unknown force when two others and the angles are known.
• Very handy in rope/string problems, supports, tension problems.
Page 5: Moments (Torque) & Couples
Moment (Torque) of a force is the turning effect of the force about a pivot or pivot point. It depends on:
The magnitude of the force (F).
The perpendicular distance (d) from the pivot to the line of action of the force.
The angle at which the force is applied (if not perpendicular, only the perpendicular component causes moment).
Moment = F × d (units: N·m)
A couple is two equal and opposite forces whose lines of action do not coincide. They produce rotation without translation. The moment of a couple depends only on the force and the distance between their lines of action; it is independent of the pivot chosen. 4
Page 6: Resultant & Equilibrant Forces
The resultant force is a single force that has the same effect as the combined effect of all forces acting on a body. It is found by vector addition of all component forces.
The equilibrant force is the force which, when added to the system, restores equilibrium. It is equal in magnitude to the resultant but opposite in direction. 5
Example: If forces of 30 N east and 40 N north act on a particle, the resultant is 50 N at angle tan⁻¹(40/30) north of east. The equilibrant is 50 N at same angle but 180° opposite (i.e., south of west in that direction).
Page 7: Centre of Gravity & Types of Equilibrium
The centre of gravity (CG) of a body is the point at which its weight appears to act. For uniform, symmetric bodies it often lies at simple geometric centres; for irregular bodies it may be found experimentally or calculated.
Types of equilibrium (for rigid bodies):
Stable Equilibrium: If when displaced slightly the body returns to its original position. CG rises when displaced (so object resists displacement). Eg a dome, a toy with wide base.
Unstable Equilibrium: If when displaced slightly the body moves further away from its original position. Eg a pencil balancing on its tip.
Neutral Equilibrium: If when displaced the body remains in its new position. Eg ring on horizontal table; wheel rolling without friction.
• Location of CG is vital for understanding tipping, balance, and design of stable structures.
• Wider base, lower CG → more stable.
• In engineering, CG calculations are used often for beams, buildings, bridges.
So far we considered concurrent forces (acting at one point). For rigid bodies, forces may act at different points, producing translation and/or rotation.
When forces do not meet at the same point, moments (torques) become important — e.g. beam supported at ends, weight in middle.
Support reactions: any support exerts normal reaction or hinge, etc.; these reaction forces contribute to both force and moment balance.
Choice of pivot: you may choose any point as pivot to calculate moments; often pick a point that eliminates unknown forces to simplify problem.
Example: A uniform beam of weight W rests on two supports at its ends. The reaction forces at supports depend on distances. Summing moments about one support gives reaction at the other, and then sum of forces gives the first reaction.
Page 9: Common Mistakes & Hints
Failing to resolve forces correctly (mix up sine & cosine).
Forgetting to use perpendicular distance for moments.
Choosing wrong pivot so that unknown reaction appears in moment sum — pick pivot smartly.
Sign conventions (clockwise vs anticlockwise moments) — be consistent.
Base of support vs centre of gravity position when discussing stability — physical base, not idealised line.
Units: ensure distances in meters if forces in Newtons to match SI; convert if problem gives different units.
