coordinate-system in robotics JNTU-H notes (ARS System)

coordinate-system in robotics JNTU-H notes (ARS System)

coordinate-system in robotics

For any industrial robot, there has to be a certain coordinate system for the proper functioning of the program. The coordinate system as defined by geometry is Cartesian Coordinate System, Polar Coordinate System, Cylindrical, or Spherical Coordinate Systems in robotics. 

Industrial robots used for medium payload have 6 Degrees of freedom & uses mostly the Cartesian Coordinate System. There is a various coordinate system in an industrial robot that follows any of the three coordinate systems & widely used among it is a Cartesian coordinate system. 

The coordinate system used in industrial robots is Rob-root, World coordinate system, Tool Coordinate System, Flange coordinate system & Base coordinate system.

The Cartesian coordinate system is a system that uniquely specifies each point in-plane by a pair of numerical coordinates, i.e. the signed distances to the point from two fixed perpendicular directed lines. 

Each reference line is known as the coordinate axis and the point where they meet is known as its origin (0, 0). The coordinates can also be defined as the perpendicular projections of the point onto the two axes also known to as signed distances from the origin. 

Fig 1 & 2 shows the illustration of the Cartesian Coordinate System. Fig 1 shows the point of intersection in space such as (-3, 1), (2, 3) & (-1.5, -2.5). 

Fig 2 shows the circle whose radius is 2 & centered at origin & illustrates the equation for the coordinate system as X2 + Y2 = 4. 

The cartesian coordinate system resembles the X, Y & Z plane in 3 Dimensional planes which can help in finding the effect of the point of intersection of that axes in space i.e. in Z plane. 

This gives the translational motions to the industrial robots i.e. X, Y & Z. 

FIG.2: ILLUSTRATION OF CARTESIAN COORDINATE SYSTEM Polar coordinate system is a 2D coordinate system. Here each point on a plane is found by a distance from a reference point and an angular distance from a reference direction. 

The reference point is analogous to the origin of a Cartesian coordinate system and is called the pole. The ray from the pole in the reference direction is known as the polar axis. 

The distance from the pole is called the radius of the coordinate and the angle is called the angular coordinate or polar angle or azimuth. Fig 3 shows the polar coordinate system whose representation in 2D is given as (3.60º) & (4, 210º).

The spherical coordinate system is a 3D space where the position of a point is specified by the radial distance, its polar and azimuth angle on a reference plane, that passes through its origin and is orthogonal to the zenith. 

The polar angle is also known as zenith angle, co-latitudes, inclination angle, or normal angle. The spherical coordinate is denoted by (r, θ, φ). Fig 4 shows the illustration of the spherical coordinate system where the X, Y, Z plane represents the (r, θ, φ) in 3D space & is resembling the radial distance, polar angle & azimuth angle. 

The spherical coordinate can be extended to a higher standard polar form also referred to as Hyper-spherical Coordinate System. 

Robot coordinate system 

The industrial robot coordinate system widely follows the Cartesian coordinate system. The most industrial robot comprises 6 Degrees of freedom i.e. 6 axes arm robot. The coordinate system for the industrial robot is Robot, World, Tool, Flange, Base coordinate system. 

Robot coordinate system: 

Robroot is the default coordinate system of the robot. Robot defines the position of the robot relative to the World Coordinate System. The origin of the robot for the RobrootCordinate system is fixed in the robot base.

World Coordinate System: 

World Coordinate System in most cases is located in the robot base. The world coordinate system is freely definable and uses the origin of Robroot& Base. It uses the Cartesian coordinate system i.e. X, Y, Z plane to define the Translational Motion of the robot axes & A, B, C to define the Rotational Motion of the robot axes with regards to the translational motion of the robot axes where X//C, Y//B, Z//A. 

Flange Coordinate System: 

Flange coordinate system is fixed at the robot flange & the origin is the center of the robot flange. It is used as the origin of the tool.

Tool Coordinate System: 

The tool coordinate system is freely definable. The origin of the tool coordinate system is called the Tool Center Point (TCP) and is used for tools.

                                    

Base Coordinate System:

The base coordinate system defines the position of the base relative to the World Coordinate System. The base coordinate system is freely definable and is used for tools &fixtures. 

Conclusion 

From the above discussion, it is clear that the Cartesian coordinate system is well suited and widely used coordinate system for industrial robots. The other coordinate systems may be used depending on the manufacturer’s way of embedding the system, but due to 3D space of Cartesian coordinate system & the use of Translational & Rotational motion relative to World coordinate system, which is best suited for 6 axes industrial robot i.e. 6 D.O.F. industrial robot, the Cartesian coordinate system is widely used for industrial robots.