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Projects, Robots and Stuff...

CPL1000 :: 3DOF Leg Inverse Kinematics

To find the angles for the servos for a specific pose, Inverse Kinematics is used. This is a relatively simple procedure for a Leg with Three Degrees of Freedom, in fact can be solved using Trigonometry. First we specify four Vectors:Latex Equation

[picture here]
Latex Equation



Unfinished
by: Chris Lane

CPL1000 :: Prototype Design

Here is the prototype design for the robot, this will be used to complete and test the inverse kinematics.

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Designed in SolidWorks

by: Chris Lane

CPL1000 :: Robot Position Forward Kinematics

Reference frames need to be attached to various parts of the robot. These are:

  1. Latex Equation = The Origin of the robot, this is not to be confused with the centre of the robot.
  2. Latex Equation = The Centre of the robot.
  3. Latex Equation = The location of the nth leg.

In order to move the body relative to the robot position kinematics need to be applied to the body of the robot. The position of the robots body is calculated using successive matrix multiplications. The first matrix defines the translation:

Latex Equation
The rotation of the body is calculated using Successive Rotations:
Latex Equation
Latex Equation

The total transformation from the Origin of the robot to the center of the base of the robot is the product of these two matrices:

Latex Equation

When these matrices are multiplied this is the result: Click Here

Each leg will have a transform Latex Equation (where n is the leg number) that describes its location relative to the center of the robot (B). This will involve a translation to the point on the body, and also a rotation for all the legs on the other side of the robot.

Latex Equation

When this is combined with the Leg Forward Position Kinematics, the total transformation from the Origin of the robot to a leg can be calculated using:

Latex Equation

This results in a very large matrixClick Here


Unfinished
Other Methods Include: Roll Pitch Yaw Euler Angles (ZYZ)
by: Chris Lane

CPL1000 :: Denavit Hartenberg Analysis of a 3DOF Leg

Overview

SolidWorks model of a three degrees of freedom leg, using model servos:
ab9a9dc23635e7494856fc3abcf76ab7

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

Procedure to transform between joints

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

  1. Rotate about the Latex Equation-axis an angle Latex Equation.
  2. Translate along Latex Equation-axis a distance of Latex Equation.
  3. Translate along Latex Equation-axis a distance of Latex Equation.
  4. Rotate Latex Equation-axis about Latex Equation-axis an angle Latex Equation.
As all the transformations are relative to the current frame, they can be post-multiplied and represented in the form:
Latex Equation
After a bit of matrix multiplication the result is: Click Here

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:
Latex Equation

Determining D-H Parameters

# Latex Equation Latex Equation Latex Equation Latex Equation
1 Latex Equation 0 0 90
2 Latex Equation 0 Latex Equation 0
3 Latex Equation 0 Latex Equation 0

These parameters can then be used to calculate the individual A matrices:
Latex Equation
Latex Equation
Latex Equation
The total transformation (Latex Equation) is very large Click Here When this result is compared to Homogeneous Transformation Matrix:
Latex Equation
The position of the end effector relative to the base can therefore be calculated:
Latex Equation
by: Chris Lane

New Book: Theory of Applied Robotics: Kinematics, Dynamics, and Control

By: Reza N. Jazar
aecc7dd1686ef4e001199adda31de50d
by: Chris Lane

New Book: Engineering Mathematics

By: K.A. Stroud, Dexter J. Booth
ee3774e894736fb4971ea01746a22552
by: Chris Lane

Blog :: Ropid Jumping Robot

I came across this very impressive robot:
by: Chris Lane

CPL1000 :: New Servos (Acoms AS-17)

I bought 20 Acoms AS-17 standard servos:
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Dimensions (mm): 18.0 x 38.0 x 37.0 Weight (grams): 36.0 Speed (sec): 0.22 Torque (Kg.cm): 2.9
by: Chris Lane

CPL1000 :: Transformation Matrices Reference

Translation Matrix:
Latex Equation
Rotation Latex Equation Axis:
Latex Equation
Rotation Latex Equation Axis:
Latex Equation
Rotation Latex Equation Axis:
Latex Equation
by: Chris Lane

CPL1000 :: Plan

The plan is to make a 6 legged robot, with 3DOF for each leg.
by: Chris Lane

New Robot: CPL1000

New Robot
by: Chris Lane