Simple linkages are capable of producing complicated motion. These techniques are also being applied to biological systems and even the study of proteins. The modern study of linkages includes the analysis and design of articulated systems that appear in robots, machine tools, and cable driven and tensegrity systems. Kaufman combined the computer's ability to rapidly compute the roots of polynomial equations with a graphical user interface to unite Freudenstein's techniques with the geometrical methods of Reuleaux and Burmester and form KINSYN, an interactive computer graphics system for linkage design Within two decades these computer techniques were integral to the analysis of complex machine systems and the control of robot manipulators. Sandor used the newly developed digital computer to solve the loop equations of a linkage and determine its dimensions for a desired function, initiating the computer-aided design of linkages. Chebyshev introduced analytical techniques for the study and invention of linkages. Burmester formalized the analysis and synthesis of linkage systems using descriptive geometry, and P. Kempe's design procedure has inspired research at the intersection of geometry and computer science.
Kempe, who showed that linkages for addition and multiplication could be assembled into a system that traced a given algebraic curve. Sylvester, who lectured on the Peaucellier linkage, which generates an exact straight line from a rotating crank. This led to the study of linkages that could generate straight lines, even if only approximately and inspired the mathematician J. This drove his search for a linkage that could transform rotation of a crank into a linear slide, and resulted in his discovery of what is called Watt's linkage. In the mid-1700s the steam engine was of growing importance, and James Watt realized that efficiency could be increased by using different cylinders for expansion and condensation of the steam. It was Leonardo da Vinci who brought an inventive energy to machines and mechanism.
Into the 1500s the work of Archimedes and Hero of Alexandria were the primary sources of machine theory. The geometric design of these systems relies on modern computer-aided design software.Īrchimedes applied geometry to the study of the lever. The skeletons of robotic systems are examples of spatial linkages. A linkage with at least one link that moves in three-dimensional space is called a spatial linkage. In these examples, the components in the linkage move in parallel planes and are called planar linkages. Interesting examples of linkages include the windshield wiper, the bicycle suspension, the leg mechanism in a walking machine and hydraulic actuators for heavy equipment. Relatively simple linkages are often used to perform complicated tasks. The internal combustion engine uses a slider-crank four-bar linkage formed from its piston, connecting rod, and crankshaft to transform power from expanding burning gases into rotary power. Examples range from the four-bar linkage used to amplify force in a bolt cutter or to provide independent suspension in an automobile, to complex linkage systems in robotic arms and walking machines. Linkages are important components of machines and tools. The fourth bar in this assembly is the ground, or frame, on which the cranks are mounted. The connecting rod is also called the coupler. The levers are called cranks, and the fulcrums are called pivots. Two levers connected by a rod so that a force applied to one is transmitted to the second is known as a four-bar linkage. The amount the force is amplified is called mechanical advantage. Because power into the lever equals the power out, a small force applied at a point far from the fulcrum (with greater velocity) equals a larger force applied at a point near the fulcrum (with less velocity). Perhaps the simplest linkage is the lever, which is a link that pivots around a fulcrum attached to ground, or a fixed point. A spatial 3 DOF linkage for joystick applications.