MindMap Gallery Differential motion and speed of robots
This figure introduces in detail the differential motion of the industrial robot coordinate system, the relationship between the differential motion of the joints and the differential motion of the terminal output. It is convenient for beginners to quickly understand the motion principles of industrial robots and lays a solid foundation for robot control.
Edited at 2023-03-21 14:35:32El cáncer de pulmón es un tumor maligno que se origina en la mucosa bronquial o las glándulas de los pulmones. Es uno de los tumores malignos con mayor morbilidad y mortalidad y mayor amenaza para la salud y la vida humana.
La diabetes es una enfermedad crónica con hiperglucemia como signo principal. Es causada principalmente por una disminución en la secreción de insulina causada por una disfunción de las células de los islotes pancreáticos, o porque el cuerpo es insensible a la acción de la insulina (es decir, resistencia a la insulina), o ambas cosas. la glucosa en la sangre es ineficaz para ser utilizada y almacenada.
El sistema digestivo es uno de los nueve sistemas principales del cuerpo humano y es el principal responsable de la ingesta, digestión, absorción y excreción de los alimentos. Consta de dos partes principales: el tracto digestivo y las glándulas digestivas.
El cáncer de pulmón es un tumor maligno que se origina en la mucosa bronquial o las glándulas de los pulmones. Es uno de los tumores malignos con mayor morbilidad y mortalidad y mayor amenaza para la salud y la vida humana.
La diabetes es una enfermedad crónica con hiperglucemia como signo principal. Es causada principalmente por una disminución en la secreción de insulina causada por una disfunción de las células de los islotes pancreáticos, o porque el cuerpo es insensible a la acción de la insulina (es decir, resistencia a la insulina), o ambas cosas. la glucosa en la sangre es ineficaz para ser utilizada y almacenada.
El sistema digestivo es uno de los nueve sistemas principales del cuerpo humano y es el principal responsable de la ingesta, digestión, absorción y excreción de los alimentos. Consta de dos partes principales: el tracto digestivo y las glándulas digestivas.
Differential motion of robot
definition
Differential motion is tiny motion. If this motion is measured or calculated over a small period of time, a velocity relationship can be obtained.
differential motion
Coordinate system differential motion (transformation)
differential translation
Trans(dx, dy, dz) to represent
Translational motion only changes the position parameters of the coordinate system, but does not change the attitude parameters.
differential rotation
Rotation about fixed reference axis
Rotation about current reference axis
Differential rotation about any axis q
analyze:
In differential motion, there are: Rot(x, δx)Rot(y, δy)=Rot(y, δy)Rot(x, δx)
In differential motion, the order of multiplications does not matter if higher order differentials are ignored
In differential motion, the order of speed can be exchanged, speed = differential motion/time
differential transformation
The differential transformation of a coordinate system is the composition of a differential translation and a differential rotation in any order. If T is used to represent the original coordinate system, and it is assumed that the change in coordinate system T caused by differential transformation is represented by dT, then there is:
Explanation of differential transformations
Each element represents the change of the corresponding element in the coordinate system
The new pose of the coordinate system after differential motion can be obtained by adding dT to the original coordinate system.
Differential operator (change): Δ
effect
1. Used to calculate the differential change of the coordinate system
2. Simplify the writing form of the differential transformation of the coordinate system
Features
1. Differential operators are not transformation matrices or coordinate systems
2. Failure to follow the required standard format
3. It is just an operator, giving the change of the coordinate system
4. It is a 4X4 matrix
expression
Differential changes between coordinate systems
Robot differential motion
Jacobian matrix
concept
The Jacobian matrix represents the geometric relationship between mechanism components at different times. It can convert the differential motion or velocity of a single joint into the differential motion or velocity of a point of interest (such as an end effector). It can also convert the motion of a single joint with Movement across the organization is linked. Since the value of the joint angle changes with time, the size of each element of the Jacobian matrix also changes with time, so the Jacobian matrix is related to time.
mathematical expression
general formula
Robot Jacobi
physical meaning
Differentiate the kinematic equations of the robot to give the impact of the joint variables at a certain moment on the posture of a certain position on the robot. This change is mainly reflected in the position change.
Features:
6X6 matrix
Differential motion of robots and robot hand coordinate systems
The relationship between Jacobian and differential operators is given
Find the relationship between the differential motion of the robot joints and the differential motion of the hand coordinate system. This relationship is a function of the robot's configuration and design, as well as the robot's position in time.
calculate
positive calculation
Each element in the Jacobian matrix is the derivative of the corresponding kinematic equation with respect to one of the variables.
Inverse calculation
Method 1: Find the inverse of the Jacobian matrix in symbolic form, then substitute the values into it and calculate the speed
Method 2: Substitute the data into the Jacobian matrix and use Gaussian elimination or other methods to find the inverse of the numerical matrix.
Method 3: Use the inverse equation of motion to calculate the speed of the joint