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:

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

Designed in SolidWorks

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

1. = The Origin of the robot, this is not to be confused with the centre of the robot.
2. = The Centre of the robot.
3. = 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:

The rotation of the body is calculated using Successive Rotations:

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:

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

Each leg will have a transform (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.

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:

This results in a very large matrixClick Here

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Other Methods Include: Roll Pitch Yaw Euler Angles (ZYZ)

Overview

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

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: 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:

Determining D-H Parameters

#
1		0	0	90
2		0		0
3		0		0

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

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

Translation Matrix: Rotation Axis: Rotation Axis: Rotation Axis:

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