Kinematics glossary with brief explanations

A mechanism in which a cam-carrying link – usually a cam plate – moves the follower via a cam joint, for example a roller lever or a tappet. The follower is held against the cam by force closure, for example by a spring, or guided in a groove by form closure. Cam mechanisms produce almost any motion, even with dwell phases, for example in packaging and textile machines. The design process works in reverse: the desired motion determines the contour of the cam plate.

In ASOM: ASOMmini calculates the cam curve from the specified motion – see Roller follower.

Springs, gas springs or counterweights balance the weight of a component so that it can be moved with little force or stays in the desired positions – for example with flaps, tailgates or beds. With springs, this is also called spring balancing. What matters is that the spring torque matches the torque due to the weight over the entire travel.

In ASOM: See the examples Kitchen cabinet flap (ASOMmini: adjusting springs for flap weights from 2 to 8 kg) and Tailgate with gas springs (ASOMv10).

A link that is not pivoted on the frame. In a four-bar linkage, it connects the two links pivoted on the frame. The component to be guided, for example a flap, is often attached to the coupler.

The path traced by a point on the coupler – the coupler point. With cleverly chosen dimensions, nearly straight or arc-like sections, cusps or loops are produced. Arc-like sections are used, for example, to make an attached link stand still temporarily.

In ASOM: Trajectories show coupler curves directly on the model, for example with the Chebyshev straight-line linkage.

Links pivoted on the frame: a crank can turn fully, while a rocker swings back and forth between two end positions. Four-bar linkages are named after these links as crank-rocker, double-crank or double-rocker; which form results is determined by the Grashof condition.

A pin or sliding block runs in a straight or curved track – the guide slot – and is guided by it.

In ASOM: In ASOMv10, spline rails form guide slots of any shape.

A position in which the coupler and the output link lie in one line; the transmission angle is then 0°. The input link reaches a limit position there, and the direction of motion of the output link is undefined – the mechanism can jam. This must be distinguished from the reversal position: if the input link and the coupler lie in one line, the output link merely reverses its direction of motion; this is not critical. Which of the two positions occurs depends on where the drive acts: when the crank and connecting rod lie in one line, this is a dead point in a combustion engine, where the piston drives, and a reversal position in a compressor, where the crank drives.

In ASOM: ASOM detects dead points during the simulation. In the drive control of ASOMv10, steps can start as soon as a dead point is reached.

Also called mobility. The number of mutually independent motions of a mechanism and thus the number of drives that uniquely determine its position. For planar mechanisms with revolute and prismatic joints, F = 3 (n − 1) − 2 g applies, where n is the number of links, counting the frame, and g is the number of joints. A four-bar linkage has F = 1. The formula applies to general dimensions; with special dimensions, the actual degree of freedom can differ.

In ASOM: ASOMv10 shows the degree of freedom of the entire model in the status bar, ASOMmini in the information bar. The excavator arm in ASOMmini has three degrees of freedom and three drives.

Specifies the motion for one degree of freedom, as an angle of rotation or a displacement over time – by a motor, a cylinder or by hand. The link whose motion the drive specifies is called the input link; the link whose motion is used is called the output link.

In ASOM: A model needs as many drives as it has degrees of freedom.

A section of the motion in which an output link is at rest while the drive keeps running – for example, so that a tool pauses briefly. Exact dwells are produced by cam mechanisms. Linkages usually achieve an approximate dwell, for example via a coupler curve, part of which follows a circular arc.

Two jointed links lie in one line: stretched out end to end in the extended position, folded over each other in the folded position. Depending on which link is driving, such a position is a reversal position or a dead point. Just short of the extended position lies the working range of the toggle mechanism.

The basic mechanism of kinematics, technically a four-link mechanism with revolute joints: four links connected by four revolute joints – the frame, two links pivoted on the frame and the coupler between them. Whether a link can turn fully is determined by the Grashof condition.

In ASOM: Four-bar linkage step by step in ASOMmini.

The stationary link on which the mechanism is mounted, for example the vehicle body, the cabinet body or the bed frame.

A spring whose force is generated by compressed gas in a cylinder. When it is compressed, its force increases slightly; the force depends on temperature and, due to internal friction, is greater during compression than during extension. Typical for tailgates and furniture flaps.

In ASOM: ASOMv10 models gas springs – see Tailgate with gas springs.

They transmit motion with a fixed transmission ratio as long as the wheels are circular. In mechanisms, they often connect two linkages or a drive to a link. Mechanisms that combine wheels and joints are called geared linkages.

In ASOM: ASOMv10 combines gear pairs, racks and belt transmissions with linkages.

It states whether a four-bar linkage has a link that can turn fully: the shortest and the longest link together must not be longer than the other two together. If the condition is met, the type depends on where the shortest link is located: if it is pivoted on the frame, the result is a crank-rocker; if it is the frame itself, a double-crank; if it is the coupler, a double-rocker with a coupler that can turn fully. If the condition is not met, no link can turn fully.

In ASOM: See the example Four-bar linkage step by step: at the end, the four-bar linkage is modified so that a link can turn fully.

The force or torque required to keep a mechanism in equilibrium in a given position – for example, the force needed to hold a flap in a half-open position.

In ASOM: In ASOMv10, you specify the desired holding forces; the load synthesis adjusts the springs so that they are achieved.

The resistance of a body to changes in its motion. Accelerated links therefore generate inertial forces and moments that increase with mass, mass moment of inertia and acceleration. In fast motion sequences, they can become greater than the forces due to weight and springs.

In ASOM: ASOMv10 takes inertia into account in the force calculation – see Piston of a two-stroke engine.

The point about which a link rotates at a given instant. Its location shifts during the motion. The locus of all instantaneous centers forms the fixed centrode in the frame and the moving centrode in the moving link; the moving centrode rolls on the fixed centrode.

In ASOM: ASOM shows the instantaneous center and the fixed and moving centrodes on the model.

The dimensions of the mechanism are known, but what is specified is the desired motion of a point or component, for example a path with a velocity profile. What is sought are the drive motions that produce it. Typical for robots and for mechanisms with several drives.

In ASOM: See the example Pick-and-place mechanism: from the path, ASOMv10 calculates the angle, velocity and torque of both drives.

The connection between two links that permits a specific relative motion. In planar mechanisms, these are mainly revolute joints and prismatic joints, plus cam joints – in which a link is guided along a cam or in a guide slot – and rolling joints, as with gears.

The force transmitted in a joint between two links. It determines the design of pins, bearings and components.

In ASOM: Joint forces appear as arrows directly on the mechanism.

Friction in a revolute joint, also called bearing friction. The friction torque increases with the joint force and the pin diameter and opposes the rotation in the joint.

In ASOM: See the example Joint friction.

Positions, displacements, velocities and accelerations of a mechanism with known dimensions are calculated for specified drive motions over the entire motion sequence.

Links connected to one another by joints. If one of the links is held fixed, that is, made the frame, the chain becomes a mechanism. Depending on which link becomes the frame, different mechanisms result from the same chain; this is called kinematic inversion.

The reverse of analysis: from requirements such as specified positions or points, the dimensions of a mechanism are determined – unlike in inverse kinematics, where the dimensions are already fixed. Strictly speaking, this is dimensional synthesis; it is preceded by the choice of type, for example a four-bar or a six-bar linkage.

In ASOM: ASOMv10 offers syntheses for one-bar, four-bar and six-bar linkages as well as slider-cranks. The requirements are maintained while you move joints and continue to optimize.

Calculation of forces and torques for a given motion. In every position, the equilibrium conditions are solved, taking into account the inertial forces resulting from the accelerations.

In ASOM: ASOMv10 and ASOMmini calculate forces kinetostatically, for every position and in real time.

The perpendicular distance between the line of action of a force and the pivot point. Force times lever arm gives the torque. In mechanisms, the lever arm changes with the position; this is why the same spring force has a varying effect over the motion sequence.

In ASOM: ASOMv10 shows lever arms on the model, measured from the instantaneous center of the link to the line of action of the force.

A component of the mechanism that is considered rigid. Depending on the number of its joints, it is called a binary, ternary or higher-order link.

A mechanism whose links are connected only by revolute and prismatic joints, that is, without cams or gears. Linkages are robust, inexpensive to manufacture and can produce a wide variety of motions.

A load case describes a condition under which a mechanism has to function, for example a particular loading. A scenario – called a load scenario in ASOM – combines everything that acts at the same time: vehicle on a slope, snow on the tailgate, −30 °C and much more.

In ASOM: ASOMv10 calculates all scenarios simultaneously and shows them in the same diagram – see Manually operated car seat.

The force a person has to apply at the handle to move a mechanism – important for comfort and ergonomics in flaps, seats or beds.

In ASOM: See the example Four-bar linkage with manual force.

In mechanism design, any device that transmits or converts motions and forces or guides components along specific paths – not just a gear transmission. In this sense, the mechanics of a flap are a mechanism as well. Transmission mechanisms pass a motion on to an output link; guidance mechanisms guide a component through specific positions. Linkages and cam mechanisms usually transmit motion non-uniformly: the ratio between input and output motion changes over the motion sequence.

A component is to assume specified positions, that is, particular locations at a particular angle, for example closed and open. The more positions are specified, the less leeway remains for choosing the joint positions. Mechanisms that guide a component through specified positions in this way are called guidance mechanisms.

In ASOM: ASOMv10 offers motion generation syntheses for one-bar, four-bar and six-bar linkages as well as slider-cranks.

The time history with which a drive specifies its angle or displacement. The sequence is usually divided into segments; for each segment, a motion law defines the curve, for example a fifth-degree polynomial. Continuous transitions in velocity and acceleration prevent impacts in the mechanism.

In ASOM: In ASOMmini, you shape the motion profile directly in the diagram – see Drive functions.

Calculates how a system of masses, springs, dampers and joints moves over time under the acting forces, with vibrations and impacts. Kinetostatics takes the opposite approach: the motion is specified, and the forces are sought. In conceptual design, kinetostatics is often sufficient because it delivers the forces immediately after every change; a multibody simulation follows in detailed design if needed.

In ASOM: ASOM calculates kinetostatically; ASOMv10 shows the forces for all scenarios simultaneously.

A component that moves about a single fixed pivot – the basic solution, for example a hinge.

In ASOM: The one-bar synthesis in ASOMv10 finds a pivot that brings the component into the desired positions or through the desired points.

A four-bar linkage in which opposite links are of equal length and form a parallelogram. The coupler moves parallel to itself without rotating – practical for steps, platforms or shelves that are to remain horizontal. When all links lie in one line (change point), it can flip into the counter-rotating antiparallelogram linkage; the design must prevent this.

In ASOM: See the example Step ladder for a motorhome: parallelogram linkage and scissor mechanism compared.

A model whose dimensions are defined as constraints and parameters. If a value is changed, the entire model adapts, and whatever is fixed is maintained.

A point on the coupler is to pass through specified points; the angular position of the coupler is left open.

In ASOM: See the example Two-point synthesis for four-bar linkages in ASOMv10.

The study of motion in a plane: positions, displacements, velocities and accelerations – initially without considering forces. “Planar” means that all points of a mechanism move in planes parallel to one another. The motion can therefore be fully represented and calculated in a single drawing plane. Many flaps, hinges, seating and reclining mechanisms have a planar design.

In ASOM: ASOM specializes in planar kinematics.

A specific planar mechanism made up of several links and joints – from a simple four-bar linkage to mechanisms with six or more links. In technical terms, it is also called a planar link mechanism or, with revolute and prismatic joints, a planar linkage. Planar kinematics describes its motion.

In ASOM: With both programs, you design and simulate planar multi-bar linkages.

Two links can only slide relative to each other along a straight line, such as a carriage on a rail or a piston in a cylinder.

Two links can only rotate relative to each other, as in a hinge or a bearing pin.

Links connected crosswise by joints like a pair of scissors. Several scissor units in a row produce a large stroke from a small installation space, for example in lift tables, aerial work platforms, ladders or couches.

In ASOM: See the example Step ladder for a motorhome: ASOMv10 designs the scissor mechanism as a six-bar linkage by means of synthesis.

A mechanism with six links and seven revolute joints – technically a six-link mechanism with revolute joints – that can produce more complex motions than a four-bar linkage, for example in furniture hinges. There are two basic forms: in the Watt chain, the two ternary links are directly connected; in the Stephenson chain, they are not. Depending on which link is the frame, different types result.

In ASOM: ASOMv10 offers syntheses for Watt and Stephenson six-bar linkages – see Symmetrical six-bar linkage for a door.

A four-link mechanism derived from the four-bar linkage by replacing the frame joint of the rocker with a prismatic joint: crank, coupler and a slider guided in a straight line. It converts rotation into reciprocating motion and vice versa, as in a piston engine.

In ASOM: See the example Piston of a two-stroke engine; ASOMv10 offers syntheses for slider-cranks.

Springs store energy and release it again. For tension and pressure springs, the spring characteristic curve describes the force over the deflection; for torsion springs, the torque over the angle. For coil springs, it is usually a straight line; its slope is called the spring rate.

In ASOM: Springs are energy stores with their own characteristic curve. ASOMmini shows which part of the characteristic curve is used – see Kitchen cabinet flap.

A mechanism guides a point, usually a coupler point, along a straight or nearly straight path without that point itself running in a rail. Well-known approximate straight-line mechanisms are those by Watt and by Chebyshev; there are also exact straight-line mechanisms, for example with a slider-crank of special dimensions.

In ASOM: See the example Chebyshev straight-line linkage in ASOMmini: with a coupler length of 20 cm, the straight section lies within a corridor of about 1 mm. ASOMv10 offers syntheses for slider-crank straight-line mechanisms, both approximate and exact.

Two jointed links that are just short of their extended position, that is, almost in line. Near the extended position, a small force across the knee produces a very large force in the longitudinal direction – used in presses, clamps and locking mechanisms. If the knee is pushed slightly past the extended position against a stop, it holds itself in place and locks.

Permissible deviations from the nominal value – for components, for example in lengths and joint positions; for springs and loads, in force. Even small deviations can noticeably change motion and forces.

In ASOM: In ASOMv10, you specify tolerances for the forces and torques of loads and springs; the evaluation shows the nominal value, minimum and maximum.

In a four-bar linkage, the angle between the coupler and the output link. The closer it is to 90°, the better the force is transmitted. As a rule of thumb, it should not drop below about 40°.