Small guide for rapid formation of manipulator (VIII): kinematic modeling (standard DH method)

Directory ：

Quick completion guide of mechanical arm （ zero ）： Main contents and analysis methods of the guide

Quick completion guide of mechanical arm （ One ）： The development of manipulator

Quick completion guide of mechanical arm （ Two ）： Application of mechanical arm

Quick completion guide of mechanical arm （ 3、 ... and ）： Mechanical structure of mechanical arm

Quick completion guide of mechanical arm （ Four ）： Reducer of key components of mechanical arm

Quick completion guide of mechanical arm （ 5、 ... and ）： End actuators

Quick completion guide of mechanical arm （ 6、 ... and ）： Stepper motor driver

Quick completion guide of mechanical arm （ 7、 ... and ）： Description method of robot arm posture

Quick completion guide of mechanical arm （ 8、 ... and ）： Kinematic modeling （ standard DH Law ）

One 、 summary

         In the last article, we have analyzed the description method of robot arm posture , Then we can officially start the kinematic analysis of it .

        Although there are not many objects that make up the manipulator , But its geometric parameters are still complex , each connecting rod The length of 、 Joint installation position and transmission mode, etc , Both affect the position and posture changes of the end of the manipulator and the joint rotation angle （ Joint variables ） The relationship between . therefore , First of all, we need to fix one on each link of the manipulator The connecting rod coordinate system , then , By describing the relationship between these connecting rod coordinate systems Terminal pose And Joint variables associated , This relationship is what we want Kinematic equation , It is obtained in the form of recursion .

        First , We need to strip the cocoon step by step , The actual manipulator is abstracted as its kinematic model , As shown in the figure below .

1.1    connecting rod

         Manipulator is a series of rigid bodies connected by joints Motion chain , When establishing kinematic equations , In order to determine the position relationship between two adjacent joint axes of the manipulator , We regard the connecting rod as a rigid body , And use the straight line in space to represent the joint axis .

        First, you need to number the connecting rod of the manipulator , We usually define a fixed base as connecting rod 0, The first movable connecting rod is connecting rod 1, And so on , The end link of the manipulator is defined as connecting rod n, As shown in the figure below .

1.2    The joints

         The motion pair formed by two components through surface contact is called Low side , The following figure shows six commonly used low pair joints .

          When designing the manipulator , We usually prefer joints with one degree of freedom . Above picture , The degrees of freedom of the rotating pair and the moving pair are the same , They correspond to rotating joints and moving joints respectively , The common representation of the two is shown in the figure below .

         As shown in the figure below ,SCARA The first three joints of the manipulator are rotary joints , The fourth joint is the mobile joint .

          It should be noted that ： The type of joint determines the type of joint variable .

Two 、Denavit-Hartenberg Law

         DH Method is a commonly used rule to define the coordinate system of connecting rod , By J Denavit,RS Hartenberg stay 1956 in .