Dynamic Models

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This page gives an overview over all implemented dynamic models.

General considerations

  • Friction is handled on axis basis. The parameters for friction are set for each axis separately.
  • Torque (Force) is always expressed in [Nm] ([N])

Rotational Axes

Dynamic Model 1 - simple rotary axis

Number Parameter Comments
1 Total moment of inertia around the rotation axis of the moved part
Model equation


Dynamic Model 2 - horizontal crank-arm axis

Horizontal crank-arm axis
Number Parameter Comments
1 Total moment of inertia around the rotation axis of the moved part
2 Square of length of crank arm (axis to payload)
Model equation


Dynamic Model 3 - vertical crank-arm axis

Vertical crank-arm axis
Number Parameter Comments
1 Total moment of inertia around the rotation axis of the moved part
2 Square of length of crank arm (axis to payload)
3 Mass (without payload) * Gravity * Distance to center of mass
4 Gravity * Distance to Payload
Model equation

Linear Axes

Dynamic Model 1 - horizontal axis

Horizontal linear axis
Number Parameter Comments
1 Total mass of the moved part.
Model equation


Dynamic Model 2 - vertical or tilted axis

Vertical linear axis
Number Parameter Comments
1 Total mass of the moved part.
2 Constant force due to gravity.
3 Gravity coefficient used to consider payload mass. (g = 9.80665)
Model equation


Dynamic Model 3 - vertical axis with a spring

Vertical linear axis with a spring
Number Parameter Comments
1 Total mass of the moved part. [kg]
2 The stiffness constant of the spring. [kg/s^2]
3 The stiffness constant times the relaxation position of the spring. [kg*m/s^2]
Model equation

Traverse Arm Robots

Dynamic Model 1

Traverse Arm robot
Number Parameter Comments
1
2
3
4
5
6
7













Scara Robots

scara robot
Robot link moment of inertia is relative to it's center of mass
Rotor moment of inertia is reflected to gearbox output shaft

The dynamic equations of the robot are expressed at the outputs of the gearboxes attached to the actuation motors. Therefore, the torques, joint positions, velocities, and accelerations are those of the gearbox output shafts.

In the following models, the variable for is the mass of link . Link is a ball screw. The variable is the lead of the ball screw, i.e. the linear distance traveled for each complete turn of the screw. The internal units of are [mm/deg], while its user units are [m/rad].

The variables and are the lengths of links and . The variables and are respectively the distances of the exes of joints and to the centers of mass of links and .

The variable for is the moment of inertia of link , relative to a reference frame attached to the link's center of mass, and about the link's axis of rotation.

Additionally, for is the moment of inertia of rotor , reflected to the gearbox output shaft as follows. Let be the moment of inertia of rotor relative to a reference frame attached to the rotor's center of mass, about the rotor's axis of rotation. Let be the gear ratio of the gearbox or pulley system, then .

The variables and are respectively the payload mass and payload moment of inertia relative to its center of mass. If no object or gripper is attached to the robot, the value of these variables is zero.

 

Dynamic Model 1

For non-coupled SCARA robots (axis 3 and 4 are not coupled) and for concentric payloads (concentric with axis 4).

Number Parameter Comments
1 kg*m2
2 kg*m2
3 kg*m2
4 kg*m2
5 kg
6 kg*m/sec2
7 kg*m2
8 kg*m2

 

 


Dynamic Model 2

For coupled SCARA robots (axis 3 and 4 are coupled) and for concentric payloads (concentric with axis 4).

Number Parameter Comments
9 kg*m2
10 kg*m2
11 kg*m2
12 kg
13 kg*m2
14 kg*m2
15 kg
16 kg*m2

 

The payload parameters for Dynamic Model 1 and Dynamic Model 2 are:

Number Parameter Comments
1 payloadMass , the mass of the payload
2 payloadInertia , the payload's moment of inertia relative to its center of mass

 





Dynamic Model 3

For coupled SCARA robots (axis 3 and 4 are coupled) and for non-concentric payloads (the payload center of mass is not located along axis 4, and is located on the x-axis of the tool flange, which is defined by the zero position of axis 4).
The dynamic parameters are the same as model 2, except for parameter No. 13.

The payload parameters are:

Number Parameter Comments
1 payloadMass , the mass of the payload
2 payloadInertia , the payload's moment of inertia relative to its center of mass
3 payloadLx the distance [m] to the center of mass from the 4th axis in the x direction
13 [kg*m2], includes the additional term in accordance with the parallel axis theorem

When using identification with this model, all of the payload parameters can be found.

 

Dynamic Model 4

Same as Dynamic Model 3.
This model is used in identification process in order to identify the payloadMass parameter only, by moving only joint number 3.

 

Dynamic Model 5

Same as Dynamic Model 3.
This model is used in identification process in order to identify the payloadInertia and payloadLx parameters, by moving only joint number 4 and very small movements in joints 1 and 2.

Delta Robots

Dynamic Model 1

Delta robot
Number Parameter Comments
1 kg*m2
2 kg*m2/sec2
3 kg
4 kg*m2
5 kg
6 kg
7 kg*m2
8 kg*m2
9 m
10 m
11
12
13
14


Puma Robots

Dynamic Model 1

Puma robot

Description:

  • - Gravity constant
  • - Mass of the ith link
  • - length of the common normal between the ith and ith+1 joints
  • - offset along z axis between the ith and ith+1 joints
  • - The distance from the ith joint to the center of mass of the ith link
Number Parameter Comments
1
kg*m^2
2 kg*m^2
3 kg*m^2
4 kg*m^2
5 kg*m^2
6 kg*m^2
7 kg*m^2
8 kg*m^2
9 kg*m^2
10 kg*m^2
11 kg*m^2
12 kg*m^2
13 kg*m^2
14 kg*m^2
15 kg*m^2
16 kg*m^2
17 kg*m^2
18 kg*m^2
19 kg*m^2
20 kg*m^2
21 kg*m^2
22 kg*m^2
23 kg*m^2

Dynamic Model 2 - Gravity

This dynamic model is for cases where the robot moves very slowly.
In such cases, the accelerations and velocities of the joints of the robot have little effect on the joints torques. The joints torques are mainly affected by gravity and friction.
This model includes only the gravity and friction part of the PUMA robot dynamic model.

Number Parameter Comments
1 kg*m^2/s^2
2 kg*m^2/s^2
3 kg*m^2/s^2
4 kg*m^2/s^2

Galileo Spherical Robots (GSR)

Dynamic Model 1

Galileo robot



Number Parameter Comments
1 mP Payload mass [kg]
2 mB Balance mass [kg]
3 TP Payload mass center distance from the flange [mm]
4 TB Balance mass center distance from the (0,0) [mm]
5 IR Inertia of the payload around roll [kg*m2