Denavit–Hartenberg Coordinate System/Parameters

  • Thread starter ConnorM
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In summary, the robot shown in the picture has four links and four joints. The links are named Base, Link 1, Link 2, and End Effector. The joints are named Joint 1, Joint 2, Joint 3, and Joint 4. The coordinate system includes a global coordinate system and four link frames. The DH parameters for the robot are also provided, including the link lengths, offsets, and angles of rotation. The differences between link offset, twist, and link length are discussed, and a hint is requested for determining the overall DH transformation from link 0 to link n.
  • #1
ConnorM
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Homework Statement


Identify the links/joints, coordinate system, and DH parameters for the robot shown in the picture.
*See attached figure

Homework Equations


Basic knowledge of DH conventions.

The Attempt at a Solution


*See attached attempts
In terms of identifying the joints and links I'm kind of confused about the difference between link offset, twist, and link length. I think the robot clearly has a Revolute-Revolute-Prismatic chain however I can't really tell if there is supposed to be another joint at the end of the prismatic joint where it turns 90deg to the manipulator.

As for the coordinate system I think it is correct, although I can't be sure without completely understanding all of the joints. One thing I'm confused about is determining whether the angle of rotation is positive or negative throughout the coordinate transformations.

It would also be helpful to get a hint towards determining the overall DH transformation for the system from link "0" - link "n"
 

Attachments

  • Robot.PNG
    Robot.PNG
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  • Robot_LinksJoints.PNG
    Robot_LinksJoints.PNG
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  • Robot_Coord.PNG
    Robot_Coord.PNG
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  • #2
as I'm not entirely sure how I'm supposed to go about this.Any help would be appreciated. Thank you.The links are:Link 0: BaseLink 1: Revolute JointLink 2: Revolute JointLink 3: Prismatic JointLink 4: End EffectorThe joints are:Joint 1: Revolute between link 0 and link 1Joint 2: Revolute between link 1 and link 2Joint 3: Prismatic between link 2 and link 3Joint 4: Revolute between link 3 and link 4The coordinate system is:X0: Global Coordinate SystemX1: Link 1 frame (rotated from X0)X2: Link 2 frame (rotated from X1)X3: Link 3 frame (translated from X2)X4: End Effector frame (rotated from X3)The DH parameters are:Link 0: a0 = 0, d1 = 0, alpha0 = 0Link 1: a1 = L1, d2 = 0, alpha1 = theta1Link 2: a2 = L2, d3 = 0, alpha2 = theta2Link 3: a3 = 0, d4 = d3, alpha3 = 0Link 4: a4 = 0, d5 = 0, alpha4 = theta3
 

Related to Denavit–Hartenberg Coordinate System/Parameters

1. What is the Denavit-Hartenberg coordinate system/parameters?

The Denavit-Hartenberg (DH) coordinate system is a mathematical framework used to describe the kinematics of a robotic or mechanical system. It consists of a set of four parameters (a, alpha, d, theta) that define the position and orientation of each joint in the system.

2. How is the DH coordinate system/parameters used in robotics?

The DH coordinate system is commonly used in robotics to model the movement and positioning of robot arms and other mechanical systems. The parameters are used to create a transformation matrix that relates the position and orientation of one joint to the next, allowing for precise control of the robot's movements.

3. What are the four parameters in the DH coordinate system?

The four parameters in the DH coordinate system are:

  • a: the distance between the current joint and the next joint along the common normal.
  • alpha: the angle between the common normal and the previous joint's z-axis.
  • d: the distance between the current joint and the next joint along the previous joint's z-axis.
  • theta: the angle between the previous joint's z-axis and the current joint's z-axis.

4. What are the advantages of using the DH coordinate system/parameters?

One of the main advantages of the DH coordinate system is its simplicity and efficiency in describing the kinematics of a robotic or mechanical system. It also allows for easy visualization and calculation of the robot's movements, making it a widely used method in robotics.

5. Are there any limitations to the DH coordinate system/parameters?

While the DH coordinate system is a useful tool for modeling robot kinematics, it does have some limitations. It assumes that all joints are revolute (rotational) and that the axes of rotation are parallel, which may not always be the case in real-world systems. Additionally, it does not account for external forces or torques acting on the system.

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