Denavit Hartenberg Analysis of a 3DOF Leg

Aug. 31, 2010 - [ robotics ]

Overview

SolidWorks model of a three degrees of freedom leg, using model servos:

[file]ab9a9dc23635e7494856fc3abcf76ab7[/file]

There are three steps for expressing a robot configuration using Denavit-Hartenberg representation:

  1. Assign a Reference Frame to each joint
  2. Define a general procedure to transform one joint to the next.
  3. Combine all transforms from the base to the TCP, to get the total transformation matrix.

Assigning Reference Frames

The configuration is represented as a series of joints and links. Reference Frames are assigned to each joint depending on certain rules:

  1. Assign each joint a number ().
  2. Assign each link a number ().
  3. an represents the common normal between and .
  4. The -axis is ignored for all joints as it is mutually perpendicular to both the and axes.
  5. If the joint is a revolute joint the direction of the -axis is dictated by the right hand rule.
  6. If the joint is a prismatic joint the -axis is in the direction of positive movement.
  7. (-axis of first joint) is parallel to the -axis of the base frame.
  8. If -axes are parallel pick -axes which are parallel.
  9. For intersection -axes pick -axis which is perpendicular to the place formed by the axes (dot product).

Procedure to transform between joints

To transform between two reference frames it takes four standard motions:

  1. Rotate about the -axis an angle .
  2. Translate along -axis a distance of .
  3. Translate along -axis a distance of .
  4. Rotate -axis about -axis an angle .
As all the transformations are relative to the current frame, they can be post-multiplied and represented in the form:

After a bit of matrix multiplication the result is: [lightbox=/latex/4fb2d317b8a8749c6b9dae217989eb53.png]Click Here[/lightbox]

Combine all transforms from base to TCP

The Transformations are all relative to the current frame therefore post-multiplied, from base of leg to foot:

Determining D-H Parameters

[table] [tr] [td]#[/td] [td][/td] [td][/td] [td][/td] [td][/td] [/tr] [tr] [td]1[/td] [td][/td] [td]0[/td] [td]0[/td] [td]90[/td] [/tr] [tr] [td]2[/td] [td][/td] [td]0[/td] [td][/td] [td]0[/td] [/tr] [tr] [td]3[/td] [td][/td] [td]0[/td] [td][/td] [td]0[/td] [/tr] [/table] [br] These parameters can then be used to calculate the individual A matrices:

The total transformation () is very large [lightbox=/latex/c3c2478bc934414dc05d410fd8b16074.png]Click Here[/lightbox] When this result is compared to Homogeneous Transformation Matrix:

The position of the end effector relative to the base can therefore be calculated:

tesing again

Aug. 30, 2010 - [ haha ]

test

testestst

Aug. 27, 2010 - [ test haha ]

test