Machine (mechanical)

Simple machines

The idea that a machine can be decomposed into simple movable elements led Archimedes to define the lever, pulley and screw as simple machines. By the time of the Renaissance this list increased to include the wheel and axle, wedge and inclined plane. The modern approach to characterizing machines focusses on the components that allow movement, known as joints.

Wedge (hand axe): Perhaps the first example of a device designed to manage power is the hand axe, also see biface and Olorgesailie. A hand axe is made by chipping stone, generally flint, to form a bifacial edge, or wedge. A wedge is a simple machine that transforms lateral force and movement of the tool into a transverse splitting force and movement of the workpiece. The available power is limited by the effort of the person using the tool, but because power is the product of force and movement, the wedge amplifies the force by reducing the movement. This amplification, or mechanical advantage is the ratio of the input speed to output speed. For a wedge this is given by 1/tanα, where α is the tip angle. The faces of a wedge are modeled as straight lines to form a sliding or prismatic joint.

Lever: The lever is another important and simple device for managing power. This is a body that pivots on a fulcrum. Because the velocity of a point farther from the pivot is greater than the velocity of a point near the pivot, forces applied far from the pivot are amplified near the pivot by the associated decrease in speed. If a is the distance from the pivot to the point where the input force is applied and b is the distance to the point where the output force is applied, then a/b is the mechanical advantage of the lever. The fulcrum of a lever is modeled as a hinged or revolute joint.

Wheel: The wheel is clearly an important early machine, such as the chariot. A wheel uses the law of the lever to reduce the force needed to overcome friction when pulling a load. To see this notice that the friction associated with pulling a load on the ground is approximately the same as the friction in a simple bearing that supports the load on the axle of a wheel. However, the wheel forms a lever that magnifies the pulling force so that it overcomes the frictional resistance in the bearing.

Mechanisms

A machine consists of an actuator input, a system of mechanisms that generate the output forces and movement, and an interface to the user. Electric motors, hydraulic and pneumatic actuators provide the input forces and movement. This input is shaped by mechanisms consisting of gears and gear trains, belt and chain drives, cam and follower mechanisms, and linkages as well as friction devices such as brakes and clutches. Structural components consist of the frame, fasteners, bearings, springs, lubricants and seals, as well as a variety of specialized machine elements such as splines, pins and keys. The user interface ranges from switches and buttons to programmable logic controllers and includes the covers that provide texture, color and styling.

Gears and gear trains

The transmission of rotation between contacting toothed wheels can be traced back to the Antikythera mechanism of Greece and the south-pointing chariot of China. Illustrations by the renaissance scientist Georgius Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth yielded a standard gear design that provides a constant speed ratio. Some important features of gears and gear trains are:

Cam and follower mechanisms

A cam and follower is formed by the direct contact of two specially shaped links. The driving link is called the cam (also see cam shaft) and the link that is driven through the direct contact of their surfaces is called the follower. The shape of the contacting surfaces of the cam and follower determines the movement of the mechanism.

Linkages

A linkage is a collection of links connected by joints. Generally, the links are the structural elements and the joints allow movement. Perhaps the single most useful example is the planar four-bar linkage. However, there are many more special linkages:

Flexure mechanisms

A flexure mechanism consists of a series of rigid bodies connected by compliant elements (also known as flexure joints) that is designed to produce a geometrically well-defined motion upon application of a force.

Structural components

A number of machine elements provide important structural functions such as the frame, bearings, splines, spring and seals.

Mechanics

Usher reports that Hero of Alexandria's treatise on Mechanics focussed on the study of lifting heavy weights. Today mechanics refers to the mathematical analysis of the forces and movement of a mechanical system, and consists of the study of the kinematics and dynamics of these systems.

Dynamics of machines

The dynamic analysis of machines begins with a rigid-body model to determine reactions at the bearings, at which point the elasticity effects are included. The rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are rigid, which means that they do not deform under the action of applied forces, simplifies the analysis by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body.

The dynamics of a rigid body system is defined by its equations of motion, which are derived using either Newtons laws of motion or Lagrangian mechanics. The solution of these equations of motion defines how the configuration of the system of rigid bodies changes as a function of time. The formulation and solution of rigid body dynamics is an important tool in the computer simulation of mechanical systems.

Kinematics of machines

The dynamic analysis of a machine requires the determination of the movement, or kinematics, of its component parts, known as kinematic analysis. The assumption that the system is an assembly of rigid components allows rotational and translational movement to be modeled mathematically as Euclidean, or rigid, transformations. This allows the position, velocity and acceleration of all points in a component to be determined from these properties for a reference point, and the angular position, angular velocity and angular acceleration of the component.

Kinematic chains

The classification of simple machines to provide a strategy for the design of new machines was developed by Franz Reuleaux, who collected and studied over 800 elementary machines. He recognized that the classical simple machines can be separated into the lever, pulley and wheel and axle that are formed by a body rotating about a hinge, and the inclined plane, wedge and screw that are similarly a block sliding on a flat surface.

Simple machines are elementary examples of kinematic chains or linkages that are used to model mechanical systems ranging from the steam engine to robot manipulators. The bearings that form the fulcrum of a lever and that allow the wheel and axle and pulleys to rotate are examples of a kinematic pair called a hinged joint. Similarly, the flat surface of an inclined plane and wedge are examples of the kinematic pair called a sliding joint. The screw is usually identified as its own kinematic pair called a helical joint.

This realization shows that it is the joints, or the connections that provide movement, that are the primary elements of a machine. Starting with four types of joints, the rotary joint, sliding joint, cam joint and gear joint, and related connections such as cables and belts, it is possible to understand a machine as an assembly of solid parts that connect these joints called a mechanism .

Two levers, or cranks, are combined into a planar four-bar linkage by attaching a link that connects the output of one crank to the input of another. Additional links can be attached to form a six-bar linkage or in series to form a robot.

Planar mechanisms

While all mechanisms in a mechanical system are three-dimensional, they can be analyzed using plane geometry, if the movement of the individual components are constrained so all point trajectories are parallel or in a series connection to a plane. In this case the system is called a planar mechanism. The kinematic analysis of planar mechanisms uses the subset of SE(3) consisting of planar rotations and translations, denote SE(2).

The group SE(2) is three-dimensional, which means that every position of a body in the plane is defined by three parameters. The parameters are often the x and y coordinates of the origin of a coordinate frame in M measured from the origin of a coordinate frame in F, and the angle measured from the x-axis in F to the x-axis in M. This is often described saying a body in the plane has three degrees-of-freedom.

The pure rotation of a hinge and the linear translation of a slider can be identified with subgroups of SE(2), and define the two joints one degree-of-freedom joints of planar mechanisms. The cam joint formed by two surfaces in sliding and rotating contact is a two degree-of-freedom joint.

Select this link to see Theo Jansen's Strandbeest walking machine with legs constructed from planar eight-bar linkages

Spherical mechanisms

It is possible to construct a mechanism such that the point trajectories in all components lie in concentric spherical shells around a fixed point. An example is the gimbaled gyroscope. These devices are called spherical mechanisms. Spherical mechanisms are constructed by connecting links with hinged joints such that the axes of each hinge passes through the same point. This point becomes center of the concentric spherical shells. The movement of these mechanisms is characterized by the group SO(3) of rotations in three-dimensional space. Other examples of spherical mechanisms are the automotive differential and the robotic wrist.

Select this link for an animation of a Spherical deployable mechanism.

The rotation group SO(3) is three-dimensional. An example of the three parameters that specify a spatial rotation are the roll, pitch and yaw angles used to define the orientation of an aircraft.

Spatial mechanisms

A mechanism in which a body moves through a general spatial movement is called a spatial mechanism. An example is the RSSR linkage, which can be viewed as a four-bar linkage in which the hinged joints of the coupler link are replaced by rod ends, also called spherical joints or ball joints. The rod ends allow the input and output cranks of the RSSR linkage to be misaligned to the point that they lie in different planes, which causes the coupler link to move in a general spatial movement. Robot arms, Stewart platforms, and humanoid robotic systems are also examples of spatial mechanisms.

Bennett's linkage is an example of a spatial overconstrained mechanism, which is constructed from four hinged joints.

The group SE(3) is six-dimensional, which means the position of a body in space is defined by six parameters. Three of the parameters define the origin of the moving reference frame relative to the fixed frame. Three other parameters define the orientation of the moving frame relative to the fixed frame.

Kinematic diagram

A kinematic diagram reduces the machine components to a skeleton diagram that emphasizes the joints and reduces the links to simple geometric elements. This diagram can also be formulated as a graph by representing the links of the mechanism as vertices and the joints as edges of the graph. This version of the kinematic diagram has proven effective in enumerating kinematic structures in the process of machine design.

An important consideration in this design process is the degree of freedom of the system of links and joints, which is determined using the Chebychev–Grübler–Kutzbach criterion.

Machine design

Machine design refers to the procedures and techniques used to address the three phases of a machine's lifecycle:

1. invention, which involves the identification of a need, development of requirements, concept generation, prototype development, manufacturing, and verification testing;
2. performance engineering involves enhancing manufacturing efficiency, reducing service and maintenance demands, adding features and improving effectiveness, and validation testing;
3. recycle is the decommissioning and disposal phase and includes recovery and reuse of materials and components.

Machine elements

The elementary mechanical components of a machine are termed machine elements. These elements consist of three basic types (i) structural components such as frame members, bearings, axles, splines, fasteners, seals, and lubricants, (ii) mechanisms that control movement in various ways such as gear trains, belt or chain drives, linkages, cam and follower systems, including brakes and clutches, and (iii) control components such as buttons, switches, indicators, sensors, actuators and computer controllers. While generally not considered to be a machine element, the shape, texture and color of covers are an important part of a machine that provide a styling and operational interface between the mechanical components of a machine and its users.