Linkage (mechanical)

A mechanical linkage is an assembly of rigid bodies (links) connected by joints (also called kinematic pairs) to form a mechanism. The links are generally assumed to be rigid, though in some analyses, flexibility is considered. The joints allow relative motion between the connected links.

The purpose of a linkage is to transmit force and motion. Linkages can be designed to transform one type of motion into another (e.g., rotary motion into linear motion), amplify or reduce forces, and control the timing and sequence of operations in a machine.

Linkages are fundamental components in a wide variety of machines and devices, ranging from simple hand tools to complex industrial machinery and robotics. Their design involves careful consideration of the desired motion, force transmission, and structural integrity.

Common types of joints used in linkages include revolute joints (allowing rotation), prismatic joints (allowing linear translation), and spherical joints (allowing three-dimensional rotation). The specific configuration of links and joints dictates the kinematic behavior of the linkage.

The analysis of mechanical linkages involves determining the relationships between the positions, velocities, and accelerations of the links. This can be achieved through various methods, including geometric analysis, kinematic equations, and computer-aided design (CAD) software.

The degree of freedom of a linkage determines the number of independent inputs required to fully define its configuration. The Gruebler's equation and Kutzbach criterion are often used to calculate the degree of freedom of planar and spatial linkages, respectively.

The design and analysis of linkages are crucial for creating efficient and reliable mechanical systems. Considerations include material selection, manufacturing processes, and maintenance requirements.