Multibody Systems
DynamicsDiscuss a project

The ideas behind
moving mechanisms.

Each entry explains one concept the way an engineer needs it: the definition, why it matters for a real design, and where it shows up in our tools and case studies.

Burmester theory

Burmester theory is the closed-form geometric method for synthesising a four-bar linkage that carries a rigid coupler body through a prescribed set of precision positions.

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Coupler curve

The coupler curve of a four-bar linkage is the trajectory traced by a single point on the coupler link as the crank rotates through one full revolution.

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DAE index 3

A differential-algebraic equation (DAE) is a system that mixes ordinary differential equations with algebraic constraints.

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Force balancing

Force balancing is the design problem of choosing counterweight masses on a moving mechanism such that the total inertia force transmitted to the ground frame is reduced — ideally to zero.

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Four-bar linkage

A planar four-bar linkage is a closed kinematic chain of four rigid links connected by four revolute (pin) joints.

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Freudenstein equation

The Freudenstein equation is the algebraic identity that ties the four link lengths of a planar four-bar to the input and output crank angles.

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Grashof condition

The Grashof condition states that a four-bar linkage will have at least one link capable of full rotation if and only if the sum of the shortest and longest links is less than or equal to the sum of the other two links (s + l ≤ p + q).

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Lagrange multiplier

In constrained Lagrangian mechanics, a Lagrange multiplier λ is the scalar (one per constraint) that enforces a holonomic constraint on the system.

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Pareto front

The Pareto front of a multi-objective optimisation problem is the set of designs for which no objective can be improved without making at least one other objective worse.

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Transmission angle

In a planar four-bar linkage the transmission angle μ is the angle between the coupler link and the rocker (output) link at their shared joint.

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