Mechanics Quiz: Joints and Links

Study Notes

Kinematic links are components that can move relative to one another in a mechanism.
Kinematic pairs are connections between links allowing relative motion, classified by their types: lower pairs (e.g., sliding, turning) and higher pairs.

A locked chain (3 links, 3 pairs, 3 joints) does not permit relative motion, acting as a rigid frame, often used in bridges.
A kinematic chain of one degree of freedom is formed with 4 links (4, 4, 4); a single link can define all others' positions.
An unconstrained chain occurs with 5 links (5, 5, 5) where relative motion is not completely defined; holds little practical significance.
A compound kinematic chain consists of more than four links and satisfies kinematic equations, allowing motion.

The degree of freedom indicates the number of independent parameters to define a mechanism's motion.
For a four-bar chain, only one variable is needed for relative positions, yielding 1 degree of freedom.
A five-bar chain requires two variables, thus having 2 degrees of freedom.
Each link generally has three degrees of freedom but loses one degree when connected to a fixed link.

Inversion of mechanisms refers to different configurations obtained by fixing various links in a kinematic chain.
Mechanisms resulting from inversions include:
- Beam engine: Converts rotary motion to reciprocating motion.
- Coupling rod of a locomotive: Transmits rotary motion between wheels.
- Watt's indicator mechanism: Traces elliptical patterns through linked motion.

Four Bar Chain: Also known as quadrilateral chain, consisting of four links and four pairs.
Single Slider Crank Chain: Combines fixed and moving links for converting motion.
Double Slider Crank Chain: Similar mechanisms allowing for linear reciprocating motion.

Kinematic Chain: Connected links that allow relative motion.
Mechanism: A kinematic chain with one or more fixed links performing a specific function.
Machine: A mechanism designed to transmit power or perform work, considering forces acting on its parts.
Structure: A rigid assembly designed to support loads, not necessarily allowing motion.

Rigid Link: Maintains shape without deformation, e.g., metal beam.
Flexible Link: Capable of motion or deformation, e.g., rubber band.
Fluid Link: Uses fluid under pressure for operation, e.g., hydraulic cylinder.

Classified based on the nature of contact, e.g., higher pairs (point/line contact) and lower pairs (surface contact like revolute and prismatic pairs).

Different types (rigid, flexible, fluid) impact the overall mobility and functionality of the mechanism.
The capacity to transmit forces effectively is essential for link performance.