# Work Space Limits

## Description

Each robot work's environment contains several frames, which has different definitions and limitations. The purpose of the Work Space Limits commands is to define each frame limitations, and combine them under all of the constraints.

## Definitions

The frames are defined as:

• World - universal frame
• Base - #{X,Y,Z,y,p,r}
• Tool - #{X,Y,Z,y,p,r}
• MachineTable - #{X,Y,Z,y,p,r}
• WorkPiece - #{X,Y,Z,y,p,r}

When # represents Cartesian point coordinate.

The robot SetPoint parameter defined as the edge point of the robot's tool. When all frames are set to #{0,0,0,0,0,0}, the robot.SetPoint command will show: SetPoint = Pb, where Pb is the vector to the robot edge relative to it's base (NOT the tool edge).

In general, the robot.SetPoint parameter is calculated as follows:
SetPoint = WorkPiece-1:MachineTable-1:Base:Pb:Tool
The relations between the frames and the Pb vector are shown here:

## Work Space Limits definition

Each frame has its own limitations. In order to define them, one should use <Frame>.command, for example:

```Base.Xmax = 150
?MachineTable.Zmin
Tool.Zmax = 1230```

 NOTE If these parameters are referred to without a frame, the parameters are set for the WORLD frame

When a move command is issued, an examination is made to check if the point doesn’t exceed the defined limits.
For Moves and Circle commands, the examination checks that the entire path doesn’t exceed the defined limits. For a Move command, only the final point is examined.

For example:

Another example:

## Limits Examination

In order to examine if a certain point is inside the allowed working area, the robot.SetPoint should be transformed into each frame, and then it should be checked that the transformed point is inside the limits of the frame.

The transformations for each frame are calculated as follows:

Frame Formula
WorkPiece CheckPoint = SetPoint = WorkPiece-1:MachineTable-1:Base:Pb:Tool

MachineTable CheckPoint = WorkPiece:SetPoint = MachineTable-1:Base:Pb:Tool

World CheckPoint = MachineTable:WorkPiece:SetPoint = Base:Pb:Tool

Base CheckPoint = Base-1:MachineTable:WorkPiece:SetPoint = Pb:Tool

Tool CheckPoint = Tool-1:Pb,0-1:Base-1:MachineTable:WorkPiece:SetPoint=Tool-1:Pb,0-1:Pb:Tool

 NOTE For the Tool frame, the absolute limits are defined relative to Pb at the time that the Tool frame limits were defined. This position is defined as Pb,0 .

The check protocol starts with World frame Base frame MachineTable frame WorkPiece frame Tool frame,
Where the check order in each frame is Xmax Xmin Ymax Ymin Zmax Zmin

 NOTE In case that the movement command isn't valid in any parameter, the program will stop checking, and raise an Error Message

## 6 Degree Of Freedom (DOF) Robot

Frame Value Xmin, Xmax Ymin, Ymax Zmin, Zmax
WorkPiece #{20,70,150,0,90,-90} -200, 200 -200, 200 -200, 200
MachineTable #{400,100,0,0,0,0} 0, 400 0, 400 0, 800
Base #{300,200,1000,0,180,180} -1000, 1000 -1000, 1000 0, 1000
Tool #{50,0,0,90, 45, 0} -200, 200 -200, 200 -200, 200
World None -1500, 1500 -1500, 1500 0, 2000

Assume that the desired SetPoint is: #{100,100,0,0,0,0} and that Pb,0 is: #{100,100,900,-45,90,0} - Is it in the work area of the limits?

Frame Formula In Limits?
WorkPiece CheckPoint = SetPoint = : #{100,100,0,0,0,0} Yes

MachineTable CheckPoint = WorkPiece:SetPoint = #{20,-30,50,0,90,-90} No - Ymin
Base CheckPoint = Base-1:MachineTable:WorkPiece:SetPoint = #{120,130,950,0,90,90} Yes

Tool CheckPoint = Tool-1:Pb,0-1:Base-1:MachineTable:WorkPiece:SetPoint = #{30,100,20,0,0,0} Yes

World CheckPoint = MachineTable:WorkPiece:SetPoint = #{420,70,50,0,90,-90} Yes

## 4 Degree Of Freedom (DOF) Robot

Frame Value Xmin, Xmax Ymin, Ymax Zmin, Zmax
WorkPiece #{100, 50, 0, 0} -100, 250 -300, 30 -200, 200
MachineTable #{320, 120, 350, 0} 0, 700 0, 500 0, 500
Base #{0, 0, 0, 0} -1000, 1000 -1000, 1000 0, 1000
Tool #{0, 20, 40, 25} -30, 20 -30, 20 -30, 20
World None -1500, 1500 -1500, 1500 0, 2000

Assume that the desired SetPoint is: #{380 , -150 , -310 , 25} and that Pb,0 is: #{780, -50, 0, 0} - Is it in the work area of the limits?

Frame Formula In Limits?
WorkPiece CheckPoint = SetPoint = : #{380 , -150 , -310 , 25} No - Xmax and Zmin

MachineTable CheckPoint = WorkPiece:SetPoint = #{480 , -100 , -310 , 25} No - Ymin and Zmin
Base CheckPoint = Base-1:MachineTable:WorkPiece:SetPoint = #{800, 20, 40, 0} Yes

Tool CheckPoint = Tool-1:Pb,0-1:Base-1:MachineTable:WorkPiece:SetPoint = #{111.762 , 3.05356 , 0 , 0} No - Xmax

World CheckPoint = MachineTable:WorkPiece:SetPoint = #{800, 20, 40, 0} Yes