The cam diagrams in Motion Sizer are based on the motion laws defined in VDI 2143. They allow you to design the motion of your axis in relation to the position of a master axis φ. Cam diagrams in Motion Sizer are used to model the movement of a servo axis, which follows the motion of a virtual line shaft. The angle of this line shaft is described by φ.
You can define segments for each cam diagram that correspond to the different sequences of motion that your axis performs.
The properties of a cam diagram provide the following parameters:
|
Parameter |
Description |
Value range |
|---|---|---|
|
Name |
A name for the selected cam diagram that is unique within the axis. |
Text |
|
Description |
Additional information related to the selected cam diagram. |
Text |
|
Units |
The unit of measure for the parameters. |
omm om oin o° (degrees) oUnit (user defined) |
|
Cycle time |
The Cycle time is available in two different units: s/cycle or cycle/min. If you enter a cycle time value in s/cycle, the cycle time value in cycle/min is automatically calculated and vice versa. The Cycle time is used to determine the velocity of the virtual line shaft, which in turn is used to establish the relationship between φ and time, which in turn is used to determine velocity, acceleration, and jerk over time. |
Number > 0 s/cycle Number > 0 cycle/min |
|
x offset |
Offset of the x axis of this cam diagram, relative to the virtual line shaft. By using this line shaft, multiple cam diagrams can be offset relative to each other. Positive and negative values are allowed. Positive value: The x axis of the cam diagram is shifted in positive direction. Negative value: The x axis of the cam diagram is shifted in negative direction. 0: The x axis of the cam diagram is not shifted. |
Positive and negative values, including 0. Unit: φ |
The properties of a segment provide several parameters. The parameters and their general descriptions are listed in this section.
The availability of each individual parameter as well as its value are determined by the values selected for the three parameters Start condition, End condition, and Motion profile. These dependencies are described in the section below.
The table describes the parameters of a cam segment. (Not all segments have all of the parameters listed. See tables further below for more details.)
|
Parameter |
Description |
Value range |
|---|---|---|
|
Name |
A name of your choice for the segment. |
Text |
|
Start condition |
The condition that applies at the start point of the segment. |
oDwell oVelocity oReversal oMotion |
|
End condition |
The condition that applies at the end point of the segment. |
oDwell oVelocity oReversal oMotion |
|
Motion profile |
The motion law describes the profile of the segment. The available motion profile depends on the Start condition and End condition selected. Refer to the list Motion Profiles Available for Combinations of Start Conditions and End Conditions. |
oStraight line oQuadratic parabola oPolynomial of the 5th degree oSimple sine oModified sine oModified acceleration trapezoid oGeneral polynomial of the 5th degree oSine and linear combined |
|
Spline interpolation mode |
This parameter is only available for user-defined motion profiles. It defines how the edge condition at the start point and end point of the profile is resolved. For further information, refer to the chapter Interpolated Profile File Format (.asc). |
oNatural spline oSpline on base of the slope of the borders oPeriodic spline |
|
Left segment edge - start section |
||
|
X |
The x coordinate of the start point of the selected cam segment. Represents the angle of the virtual line shaft where the segment starts. |
Decimal number Unit: φ |
|
Y |
The y coordinate of the start point of the selected cam segment. Represents the position of the axis at the segment start. This is the value of s at the position x. |
Decimal number Unit: Position |
|
Slope |
The slope of the position curve at the start point of the selected cam segment. This is the value of s’. |
Decimal number Unit: Position / φ |
|
Curvature |
The curvature of the position curve at the start point of the selected cam segment. This is the value of s’’. |
Decimal number Unit: Position / φ2 |
|
Right segment edge - end section |
||
|
X |
The x coordinate of the end point of the selected cam segment. Represents the angle of the virtual line shaft where the segment ends. |
Decimal number Unit: φ |
|
Y |
The y coordinate of the end point of the selected cam segment. Represents the position of the axis at the segment end. This is the value of s at the position x. |
Decimal number Unit: Position |
|
Slope |
The slope of the position curve at the end point of the selected cam segment. This is the value of s’. |
Decimal number Unit: Position / φ |
|
Curvature |
The curvature of the position curve at the end point of the selected cam segment. This is the value of s’’. |
Decimal number Unit: Position / φ2 |
|
C |
Defines the fraction of the selected cam segment that is spent for changing the velocity. The value 1 indicates that there is no constant velocity phase within the segment. Acceleration and deceleration procedures are performed throughout the segment. The value 0.5, for example, indicates that acceleration and deceleration procedures are performed during the half of the segment time. The other half of the segment, the inflexion point between acceleration and deceleration, is reserved for constant velocity. |
0...1 |
|
Lambda |
Defines the position of the inflexion point (when C=1) or of the phase within constant velocity (when C<1) on the x axis (φ) within the selected cam segment. Lambda describes the proportion between acceleration and deceleration on the virtual line shaft angle within the segment. In a segment that only consists of an acceleration phase (Start condition = Dwell, End condition = Velocity, the Lambda value is fixed to 1. This means that 100% of the time of changing the velocity is used for acceleration, 0% is used for deceleration. In a segment that only consists of a deceleration phase (Start condition = Velocity, End condition = Dwell, the Lambda value is fixed to 0. This means that 0% of the time of changing the velocity is used for acceleration, 100% is used for deceleration. In a segment that only consists of acceleration and deceleration phases (Start condition = Dwell, End condition = Dwell, the Lambda value is greater than 0 and less than 1. A value of 0.5 means that acceleration and deceleration phases have the same length on the x axis (φ). 50% of the total length is spent with changing the velocity. A value 0f 0.1 means that 10% of the acceleration and deceleration length on the x axis (φ) are used for deceleration. 90% are used for acceleration. |
0...1 |
Motion Profiles Available for Combinations of Start Conditions and End Conditions
Depending on the combination of the boundary conditions (start condition, end condition), the following Motion profile values are available.
|
From/to |
Dwell (v=0, a=0) |
Velocity (v<>0, a=0) |
Reversal (v=0, a<>0) |
Motion (v<>0, a<>0) |
|---|---|---|---|---|
|
Dwell (v=0, a=0) |
Straight line Quadratic parabola Polynomial of the 5th degree Simple sine Modified sinoidal Modified acceleration trapezoid General polynomial of the 5th degree |
Quadratic parabola Polynomial of the 5th degree Simple sine Modified sinoidal Modified acceleration trapezoid General polynomial of the 5th degree (Lambda = 1) |
General polynomial of the 5th degree |
General polynomial of the 5th degree |
|
Velocity (v<>0, a=0) |
Quadratic parabola Polynomial of the 5th degree Simple sine Modified sinoidal Modified acceleration trapezoid General polynomial of the 5th degree (Lambda = 0) |
Straight line General polynomial of the 5th degree |
General polynomial of the 5th degree |
General polynomial of the 5th degree |
|
Reversal (v=0, a<>0) |
General polynomial of the 5th degree |
Sine and linear combined General polynomial of the 5th degree |
General polynomial of the 5th degree |
|
|
Motion (v<>0, a<>0) |
General polynomial of the 5th degree |
|||
Parameters for Motion Laws Quadratic parabola, Polynomial of the 5th degree, Simple sine, Modified sine, Modified acceleration trapezoid
The table lists the parameters that are available for the motion laws Quadratic parabola, Polynomial of the 5th degree, Simple sine, Modified sine, Modified acceleration trapezoid, and the values they can have in accordance with the selected Start condition and End condition:
|
Parameter |
Start condition - End condition |
||
|---|---|---|---|
|
Dwell - Dwell |
Dwell - Velocity |
Velocity - Dwell |
|
|
X start |
User input |
User input |
User input |
|
Y start |
User input |
User input* or calculated by Motion Sizer |
User input* or calculated by Motion Sizer |
|
Slope start |
Fixed to 0 |
Fixed to 0 |
User input or calculated by Motion Sizer* |
|
Curvature start |
Fixed to 0 |
Fixed to 0 |
Fixed to 0 |
|
X end |
User input |
User input |
User input |
|
Y end |
User input |
User input* or calculated by Motion Sizer |
User input* or calculated by Motion Sizer. |
|
Slope end |
Fixed to 0 |
User input or calculated* by Motion Sizer. |
Fixed to 0 |
|
Curvature end |
Fixed to 0 |
Fixed to 0 |
Fixed to 0 |
|
C |
User input(0...1) |
User input* (0...1) or calculated by Motion Sizer. |
User input* (0...1) or calculated by Motion Sizer. |
|
Lambda |
User input(0...1) |
Fixed to 1 |
Fixed to 0 |
|
* By default, one out of four parameters is calculated by Motion Sizer, whereas the other three parameters are editable.You can change this by clicking the option next to the parameter. |
|||
Parameters for Motion Law Straight line
The table lists the parameters that are available for the motion law Straight line and the values they can have in accordance with the selected Start condition and End condition:
|
Parameter |
Start condition - End condition |
|
|---|---|---|
|
Dwell - Dwell |
Velocity - Velocity |
|
|
X start |
User input |
User input |
|
Y start |
User input |
User input* or calculated by Motion Sizer |
|
Slope start |
Fixed to 0 |
User input or calculated* by Motion Sizer |
|
Curvature start |
Fixed to 0 |
Fixed to 0 |
|
X end |
User input |
User input |
|
Y end |
User input |
User input* or calculated by Motion Sizer |
|
Slope end |
Fixed to 0 |
The same value is used as for the parameter Slope start. |
|
Curvature end |
Fixed to 0 |
Fixed to 0 |
|
* By default, the Slope start parameter is calculated by Motion Sizer, whereas the parameters Y start and Y end are editable.You can change this by clicking the option next to the parameter. |
||
Parameters for Motion Law Sine and linear combined
The motion law Sine and linear combined is only available for Start condition > Reversal and End condition > Reversal. The table lists the available parameters:
|
Parameter |
Start condition - End condition |
|---|---|
|
Reversal - Reversal |
|
|
X start |
User input |
|
Y start |
User input |
|
Slope start |
User input* or calculated by Motion Sizer |
|
Curvature start |
User input* or calculated by Motion Sizer |
|
X end |
User input |
|
Y end |
User input |
|
Slope end |
User input* or calculated by Motion Sizer |
|
Curvature end |
User input* or calculated by Motion Sizer |
|
C |
User input* or calculated by Motion Sizer |
|
Lambda |
User input* or calculated by Motion Sizer |
|
* Use the Input parameters list to select two out of six parameters as editable. The remaining four parameters are calculated by Motion Sizer. |
|
Parameters for Motion Law General polynomial of the 5th degree
Since the motion law General polynomial of the 5th degree is available for 15 combinations of Start condition - End condition values, 4 different parameter tables are provided for this motion law.
The table lists the parameters that are available for the motion law General polynomial of the 5th degree and the values they can have in accordance with the selected Start condition=Dwell together with several End condition values:
|
Parameter |
Start condition - End condition |
|||
|---|---|---|---|---|
|
Dwell - Dwell |
Dwell - Velocity |
Dwell - Motion |
Dwell - Reversal |
|
|
X start |
User input |
User input |
User input |
User input |
|
Y start |
User input |
User input |
User input |
User input |
|
Slope start |
Fixed to 0 |
Fixed to 0 |
Fixed to 0 |
Fixed to 0 |
|
Curvature start |
Fixed to 0 |
Fixed to 0 |
Fixed to 0 |
Fixed to 0 |
|
X end |
User input |
User input |
User input |
User input |
|
Y end |
User input |
User input |
User input |
User input |
|
Slope end |
Fixed to 0 |
User input |
User input |
Fixed to 0 |
|
Curvature end |
Fixed to 0 |
Fixed to 0 |
User input |
User input |
The table lists the parameters that are available for the motion law General polynomial of the 5th degree and the values they can have in accordance with the selected Start condition=Motion together with several End condition values:
|
Parameter |
Start condition - End condition |
|||
|---|---|---|---|---|
|
Motion - Dwell |
Motion - Motion |
Motion - Reversal |
Motion - Velocity |
|
|
X start |
User input |
User input |
User input |
User input |
|
Y start |
User input |
User input |
User input |
User input |
|
Slope start |
User input |
User input |
User input |
User input |
|
Curvature start |
User input |
User input |
User input |
User input |
|
X end |
User input |
User input |
User input |
User input |
|
Y end |
User input |
User input |
User input |
User input |
|
Slope end |
Fixed to 0 |
User input |
Fixed to 0 |
User input |
|
Curvature end |
Fixed to 0 |
User input |
User input |
Fixed to 0 |
The table lists the parameters that are available for the motion law General polynomial of the 5th degree and the values they can have in accordance with the selected Start condition=Reversal together with several End condition values:
|
Parameter |
Start condition - End condition |
|||
|---|---|---|---|---|
|
Reversal - Dwell |
Reversal - Motion |
Reversal - Reversal |
Reversal - Velocity |
|
|
X start |
User input |
User input |
User input |
User input |
|
Y start |
User input |
User input |
User input |
User input |
|
Slope start |
Fixed to 0 |
Fixed to 0 |
Fixed to 0 |
Fixed to 0 |
|
Curvature start |
User input |
User input |
User input |
User input |
|
X end |
User input |
User input |
User input |
User input |
|
Y end |
User input |
User input |
User input |
User input |
|
Slope end |
Fixed to 0 |
User input |
Fixed to 0 |
User input |
|
Curvature end |
Fixed to 0 |
User input |
User input |
Fixed to 0 |
The table lists the parameters that are available for the motion law General polynomial of the 5th degree and the values they can have in accordance with the selected Start condition=Velocity together with several End condition values:
|
Parameter |
Start condition - End condition |
|||
|---|---|---|---|---|
|
Velocity - Dwell |
Velocity - Motion |
Velocity - Reversal |
Velocity - Velocity |
|
|
X start |
User input |
User input |
User input |
User input |
|
Y start |
User input |
User input |
User input |
User input |
|
Slope start |
User input |
User input |
User input |
User input |
|
Curvature start |
Fixed to 0 |
Fixed to 0 |
Fixed to 0 |
Fixed to 0 |
|
X end |
User input |
User input |
User input |
User input |
|
Y end |
User input |
User input |
User input |
User input |
|
Slope end |
Fixed to 0 |
User input |
Fixed to 0 |
User input |
|
Curvature end |
Fixed to 0 |
User input |
User input |
Fixed to 0 |
