Theory of Machines
A mechanism is a set of rigid bodies whose joints remove exactly enough freedom to leave the motion you wanted. These topics animate the motion rather than describing it, which is the only way a linkage ever makes sense.
Start from the beginning →9 topics you can watch now, 10 still to come.
Mechanisms and mobility
Links, pairs, and how many inputs a mechanism needs.
- Links, Pairs and Degrees of FreedomStart here. Take three bars in a plane and add joints one at a time, watching nine freedoms fall to one.
- Four-Bar Mechanisms and InversionsOne inequality decides whether a motor can drive a linkage at all — and fixing a different link of the same chain gives a completely different machine.
- Kinematic pairs and their classification
- Straight-line and steering mechanisms
Velocity and acceleration analysis
Where each point of a moving linkage is going, and how fast.
- Klein's construction
- Analytical loop-closure methods
Cams and followers
Designing a shape so that motion comes out the way you specified.
- Cam profile construction step by step
- Polynomial and modified motion laws
Gears and gear trains
Transmitting rotation at a fixed ratio, without slip.
- Helical, bevel and worm gearing
- Gear tooth stress and AGMA rating
Dynamics of machinery
The forces a moving machine puts back into its own frame.
- Flywheels and GovernorsTwo devices that both regulate speed and solve completely different problems — one smooths within a cycle, the other corrects across many.
- BalancingA rotor can sit perfectly still on knife edges and shake a machine apart when it spins. Static balance is not merely incomplete — it is misleading.
- Vibration and WhirlingA shaft that bows out at its critical speed and straightens again above it — which is why turbines are run through their criticals rather than below them.
- Gyroscopic EffectsThe one topic where the answer is at right angles to the question. Derived from angular momentum, so the direction comes out right every time.
- Static and dynamic force analysis of linkages
- Governor characteristics: sensitivity, stability and effort
About Theory of Machines
Theory of machines is about mechanisms: assemblies of rigid parts arranged so that motion goes in deliberately. Before any force is considered, the question is what movement the geometry permits at all, which is what degrees of freedom counts.
The four-bar linkage is the subject's workhorse and worth real attention, because a startling range of machines is a four-bar in disguise. Change one link length and a mechanism that rocks becomes one that rotates fully. Cams take the same idea further, encoding an arbitrary motion profile as a shaped surface.
Then the parts start moving fast, and dynamics arrives: unbalanced rotating mass becomes vibration, stored rotational energy becomes a flywheel's smoothing effect, and a spinning body resists reorientation in a way that feels wrong until you have seen it.
What to know first
- Mechanics — statics, and velocity and acceleration of rigid bodies
- Basic trigonometry and vectors
Where it gets used
- Recognising a linkage in engines, suspensions, presses and robotics
- Diagnosing machine vibration as a balancing problem
- Designing a cam profile for a required motion