Motion Profiles

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Motion Profiles

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You can choose out of a number of predefined motion profiles in the Motion Profile Wizard.

Flat
Ramp
Trapezoidal
Partial Trapezoidal
Geneva Mechanism
Sine
Cubic
Partial Cubic
Cycloidal
Standard Modified Sine
Modified Trapezoidal
Modified Sine with Constant Velocity (MSC50)
General Modified Sine with Constant Velocity (MSC%)
3-4-5 Polynomial
1-3-5-7-9 Polynomial

Flat

The flat profile is a zero order profile. It has a constant position, zero velocity and acceleration.

Ramp

The ramp profile is a first order profile. It has a constant velocity and acceleration peaks at the start and end of the motion.

Ramp

The ramp profile.

Trapezoidal

The trapezoidal profile is a second order profile. It has a constant acceleration at the start of the motion and a constant deceleration at the end of the motion.

Trapezoidal

The trapezoidal profile.

This profile is most widely used in early servo systems. Because of the discontinuity in the acceleration this motion profile can still induce a lot of vibrations. Therefore in modern servo systems third order profiles are preferred.

Partial Trapezoidal

The partial trapezoidal profile is a second order profile. It has is equal to the trapezoidal motion, but has a constant velocity part, during a fraction CV (%) of the motion.

PartialTrapezoidal

The partial trapezoidal profile.

Geneva Mechanism

A Geneva mechanism is an old motion profile generation mechanism. A continuously rotating crankshaft (a) generates an intermittent motion of a second shaft (b). The result is a second order profile.

Geneva

A Geneva mechanism.

The motion profile generator yields the motion of the second shaft (b). It is shown below:

GenevaMechanism

The Geneva mechanism profile.

Sine

The sine profile is a second order profile of which the displacement can be described as:

x = 0.5 - cos (p * t) / 2.

Sine

The sine profile.

Cubic

The cubic profile is a third order profile of which the acceleration is constantly increasing and decreasing.

Cubic

The cubic profile.

Partial Cubic

The partial cubic profile (3rd order) is a modified cubic profile with a constant velocity during a fraction CV (%) of the motion and a constant acceleration during a fraction CA (%) of the motion.

PartialCubic

The partial cubic profile.

Cycloidal

The cycloidal profile is a third order profile, of which the velocity can be described as:

v = stroke*(1-cos(t*a))

Cycloidal

The cycloidal profile.

Modified Sine

The modified sine profile is also a third order profile. It is a modification of the cycloidal profile to get a lower maximum velocity and a lower maximum acceleration.

ModifiedSine

The modified sine profile.

Modified Trapezoidal

The modified trapezoidal profile is a modification of the trapezoidal profile (to make it a third order profile). This profile yields a very low maximum acceleration.

ModifiedTrapezoidal

The modified trapezoidal profile.

Modified Sine with Constant Velocity (MSC50)

The modified sine with constant velocity profile (3rd order) is a modification of the modified sine profile. It has a constant velocity during 50% of the motion.

ModifiedSineConstantVelocity

The modified sine with constant velocity profile.

General Modified Sine with Constant Velocity (MSC%)

The modified sine with constant velocity profile (3rd order) is a modification of the modified sine profile. It has a constant velocity during a user definable part of the of the motion. The non-zero acceleration part is defined by two parameters which are both defined as a fraction of the motion. The first parameters alpha (%) defines the start of the acceleration and the second parameters n (%) defines the end of the acceleration.

GeneralModifiedSineConstantVelocity

The general modified sine with constant velocity profile.

3-4-5 Polynomial

The is a third profile described by a 5th order polynomial.

345Polynomial

The 1-3-5 polynomial profile.

1-3-5-7-9 Polynomial

The is a third/fourth order profile described by a 9th order polynomial. The profile is characterized by two parameters that denote the initial jerk, BB, and the crossover jerk, BM. If BB is chosen zero, this a a fourth order profile. If BB is chosen non-zero, this is a third order profile.

13579Polynomial

The 1-3-5-7-9 polynomial profile.

To keep the polynomial consistent, i.e. the polynomial does not change when the amplitude is changed, the initial jerk (BB) and the crossover jerk (BM) are defined for a standard motion with:

stroke = 1
start_time = 0
stop_time = 1

Comparison of Profiles

The specific shape of a motion profile can have a significant influence on the dynamic behavior. Some profiles minimize the maximum velocity, some profile minimize acceleration, while other profiles tend to make a tradeoff between the maximum velocity and acceleration. If we take a standard motion with stroke 1 and motion time 1 sec., the following table can be generated:

profile

order

vmax

amax

j(0)

j(1/2)

Flat

0

0

0

0

0

Ramp

1

1

infinite

infinite

0

Trapezoidal

2

2

4

infinite

-infinite

Partial Trapezoidal1

2

1.67

4.17

infinite

0

Geneva Mechanism

2

2.41

8.49

infinite

-118.5

Sine

2

1.57

4.93

infinite

-15.5

Cubic

3

2

4

32

-32

Partial Cubic3

3

1.67

5.55

55.6

0

Cycloidal

3

2

6.28

39.5

-39.5

Modified Sine

3

1.76

5.53

69.4

-23.2

Modified Trapezoidal

3

2

4.88

61.4

-61.4

MSC50

3

1.26

9.20

173.6

0

MSC%4

3

1.37

7.20

113.1

0

3-4-5 Polynomial

3

1.88

5.77

60

-30

1-3-5-7-9 Polynomial5

3/4

2.05

10.25

BB

BM

1: Parameter CV = 20%

2: For lw >> lc the Crank Rod profile equals the sine profile, for lw > lc performance deteriorates.

3: Parameter CV = 20%, CA = 20%

4: Parameter n = 30%, alpha = 10%

5: Parameter BB = 30%, BM = 10%

Here j(0) is the initial jerk yerk (derivative of acceleration) and j(1/2) the crossover (halftime) jerk.