Today, Zmotion brings how to draw the pentagram through two-axis linear interpolation.
Here are word description, routine codes simulation displaying and video showing.
Let’s see the details.
XPLC864E2 is a kind of multi-axis economical bus motion controller, and the volume of XPLC864E2 is small but the communication function is full. It supports RS232 serial port, RS485 serial port, network port, CAN bus and EtherCAT bus to connect to external equipment. For multiple network channels, it can be extended through the interchanger.
In addition, XPLC864E2 motion controller supports using pulse axes and bus axes mixed, and there are 8 motor axes totally. Except EtherCAT interface, outputs can be configured as 8 pulse signal outputs. And there are two encoder inputs, which are configured by input.
Even though, XPLC864E2 only has 8 motor axes, it can be extended to 12 axes to achieve linear interpolation, electronic cam, electronic gear, synchronization follow, virtual axis setting, etc.
What's more, for XPLC series motion controllers, they can be used in all kinds of applications that are online or offline.
(1) method and principle
The linear interpolation algorithm adopts the data sampling method. Specifically, it uses a small straight line to approach the given trajectory. And then the distance to be moved by each axis in the next interpolation period will be output, which means it is not necessary to interpolate once for each pulse equivalent, the high feed rates can be achieved.
Data sampling method is used by linear interpolation as mentioned above, but what is it?
Actually, the principle is to use the idea of time division, that is, according to the feed speed f and the interpolation period t, divide the profile curve into sections of the profile step length I, I=ft, and then calculate the coordinate increment of each axis participating in the interpolation motion in each interpolation cycle.
(2) what is linear interpolation
A. linear interpolation features
Firstly, let's see the motion process.
It selects the axis number/axis group through the "BASE" command, then controls the multi-axis linkage, the linear motion is completed.
The first axis selected by BASE is the main axis, and axis parameters of interpolation all use main axis parameters, such as, UNITS, SPEED, etc., then send "MOVE" linear interpolation instruction, it will execute in sequence in main axis' motion buffer area. If you need to cancel linear interpolation, using CANCEL command to achieve emergency stop.
Main Features:
--support 16 axes linear interpolation--
base(0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)
--support multi-channel interpolate synchronously
BASE(0,1)
MOVE(100,200)
BASE(2,3,4)
MOVE(30,40,50)
(3) how to calculate parameters
Here, we take 2-axis linear interpolation as example, axis 0 and axis participate in linear interpolation motion, please see below graphic.
In the plane, it moves from point A to point B, axis X and axis Y open at the same time, and achieve the end point synchronously.
Set motion distance of axis 0 is ∆ X, set motion distance of axis 1 is ∆ Y. The master axis is axis 0 (the first axis of main axis), so interpolation all adopt parameters of axis 0.
If the main axis motion speed of interpolation is S (set speed of axis 0), then actual speed of each axis is the separate speed of main axis, which means they don't equal to S, at this time:
Distance of interpolation: X=[(∆X)2+(∆Y)2]½
Actual speed of axis 0: S0=S× ∆ X/X
Actual speed of axis 1: S1=S× ∆ X/X
(4) how to achieve linear interpolation
There is linear interpolation algorithm built in XPLC864E2, it supports 8 EtherCAT bus axes to do linkage linear interpolation, 12 axes can be expanded, use MOVE linear interpolation instruction, it is easy to complete interpolation effectively.
A. Instructions related to linear interpolation
--MOVE: send pulse to drive, achieve linear interpolation.
Grammar:
MOVE(distance1 [,distance2[,distance3 [,distance4...]]])
MOVEABS(distance1 [,distance2 [,distance3 [,distance4...]]])
MOVESP(distance1 [,distance2 [,distance3 [,distance4...]]])
MOVEABSSP(distance1 [,distance2 [,distance3 [,distance4...]]])
--BASE: select which axis to participate in interpolation, namely, send MOVE to which axes.
Grammar:
BASE(axis1 [,axis 2 [,axis 3 [,axis 4...]]])
--SPEED_RATIO: the interpolation motion speed ratio is controlled freely, the current speed = SPEED * SPEED_RATIO.
Grammar:
SPEED_RATIO(axis No.) = value
--MOVE_PAUSE: motion pause and resume, MOVE_PAUSE is to pause, MOVE_RESUME is to resume.
Grammar:
MOVE_PAUSE(mode)
--C ANCEL: cancel motion, axis / axis group decelerates to stop, CANCEL(2) means emergency stop, RAPIDSTOP(2) means all axes stop rapidly.
Grammar:
CANCEL(mode) AXIS (main axis), RAPIDSTOP(mode)
B. Types of linear interpolation
--3 forms can be selected--
MOVE: relative motion
The distance parameter of interpolation is the relative distance to current interpolation starting point, SPEED speed parameter is used.
For example:
MOVEABS: absolute motion
The distance parameter of interpolation is the absolute distance to origin point, ABS suffix is added behind MOVE relative motion instruction, and SPEED speed parameter is used.
For example:
MOVESP/MOVEABSSP
The instructions that are with SP use FROCE_SPEED to set speed parameter compulsively to move, not the SPEED. It only needs to add SP suffix behind MOVE or MOVEABS. And FORCE_SPEED parameter can enter motion buffer area to achieve dynamic speed.
Example 1 (SP instruction):
C. Other examples.
--MOVESP dynamic speed--
MOVESP linear interpolation motion uses the speed set by FORCE_SPEED instruction, and starting speed of each SP motion can be customized through STARTMOVE_SPPED, ending speed of each SP motion can be customized through ENDMOVE_SPPED, please note when they are not used, set bigger values.
Codes:
Curve:
when speed is 0, it starts to move for completing three linear interpolation motions. The first motion's speed is 50, the second is 60 and the third one is 80.
--Speed ratio control--
In linear interpolation motion, SPEED_RATIO can be used to set the ratio of current motion speed, make current motion speed = SPEED*SPEED_RATIO, and when the instruction was sent out, the command will take effect at once. Therefore, dynamic speed can be achieved through this command.
Codes:
Curve:
--Pause and resume--
MOVE_PAUSE is used to pause the motion, there are several modes:
Codes:
Curve:
(1) two axes continuous interpolation is to complete "pentagram".
Routine codes:
Sampled waveform:
Sampled 2-axis interpolation trajectory:
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