In applied mathematics

Applied mathematics

Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...

 as used in the engineering field of robotics

Robotics

Robotics is the branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots...

, an arm solution is a solution of equations that allow the calculation of the precise design parameters of a robot's arms in such a way as to enable it to make certain movements.

A typical industrial robot

Industrial robot

An industrial robot is defined by ISO as an automatically controlled, reprogrammable, multipurpose manipulator programmable in three or more axes...

 is built with fixed length segments that are connected either at joints whose angle

Angle

In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

s can be controlled, or along linear slides whose length can be controlled. If each angle and slide distance

Distance

Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...

 is known, the position and orientation of the end of the robot arm relative to the base can be computed with the simple trigonometry

Trigonometry

Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...

 in robot control

Robot control

-See also:* Control theory* Mobile robot navigation* Robot kinematics* Simultaneous localization and mapping* Robot locomotion* Motion planning* Robot learning* Vision Based Robot Control...

.

Going the other way — calculating the angles and slides needed to achieve a desired position and orientation — is much harder. The mathematical procedure for doing this is called an arm solution. For some robot designs, such as the Stanford arm, SCARA robot or cartesian coordinate robot

Cartesian coordinate robot

A cartesian coordinate robot is an industrial robot whose three principal axes of control are linear and are at right angles to each other. Among other advantages, this mechanical arrangement simplifies the Robot control arm solution...

s, this can be done in closed form

Closed-form expression

In mathematics, an expression is said to be a closed-form expression if it can be expressed analytically in terms of a bounded number of certain "well-known" functions...

. Other robot designs require an iterative

Iterative method

In computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems. A specific implementation of an iterative method, including the termination criteria, is an algorithm of the iterative method...

solution.

External links

• infolab.stanford.edu - The Stanford Arm (1969), with a configuration such that the mathematical computations (arm solutions) were simplified to speed up computations