Lecture 3 - Forward Kinematics

What is Forward Kinematics?

Determining the position and orientation ( pose) of the end-effector with respect to the base as a function of each joint motion ( $q$ which is either $θ$ or $d$ )

Kinematic Chains

Transformations

Going to the next frame ( $i$ ) from the previous frame ( $i - 1$ )

A_{i} = R_{i}^{i - 1} 0 d_{i}^{i - 1} 1

Going to the end-effector frame ( $n$ ) from the base frame ( $0$ )

H_{n}^{0} = i = 1 \prod i = n A_{i} (q_{i})

Forward Kinematics Approaches

Geometric Approach

Suitable for simple problems
Suitable for getting the position of the end effector only, not orientation

DH Convention

Frames

Assign axes on the joints
Assign axes on the last important link (manipulator)

Transformation Parameters

We are just moving from the origin of the current frame to the origin of the next frame

It’s like asking: how can we make the current frame become in the same orientation and position as the next frame?

We just do it in 4 steps

Motion	Parameter	Name
Rotating around the current z axis to make the x axis of the current frame parallel to the x axis of the next frame	$θ$	Joint angle
Translating along the current z axis to intersect with the x axis of the next frame	$d$	Joint offset
Translating along the new x axis (x axis of the next frame) to arrive at the origin of the next frame	$a$	Link length
Rotating around the new x axis of the next frame to make the current z axis align with the next z axis	$α$	Link twist

T_{i}^{i - 1} = T_{R o t, z_{i - 1}, θ_{i}} T_{T r an, z_{i - 1}, d_{i}} T_{T r an, x_{i}, a_{i}} T_{R o t, x_{i}, α_{i}}

This results in a total homogenous transformation matrix from frame $i - 1$ to frame $i$

To get the transformation from the base frame to the end effector frame we just multiply the transformations between each two frames together

T_{n}^{0} = T_{1}^{0} T_{2}^{1} T_{3}^{2} \dots T_{n - 2}^{n - 3} T_{n - 1}^{n - 2} T_{n}^{n - 1}

📖 ASUPEDIA

Explorer

Lecture 3 - Forward Kinematics

What is Forward Kinematics?

Kinematic Chains

Transformations

Going to the next frame ( $i$ ) from the previous frame ( $i - 1$ )

Going to the end-effector frame ( $n$ ) from the base frame ( $0$ )

Forward Kinematics Approaches

Geometric Approach

DH Convention

Frames

Transformation Parameters

Resources

Lectures

YouTube Channels

Examples

Videos

Extra

Graph View

Table of Contents

📖 ASUPEDIA

Explorer

Lecture 3 - Forward Kinematics

What is Forward Kinematics?

Kinematic Chains

Transformations

Going to the next frame (i) from the previous frame (i−1)

Going to the end-effector frame (n) from the base frame (0)

Forward Kinematics Approaches

Geometric Approach

DH Convention

Frames

Transformation Parameters

Resources

Lectures

YouTube Channels

Examples

Videos

Extra

Graph View

Table of Contents

Going to the next frame ( $i$ ) from the previous frame ( $i - 1$ )

Going to the end-effector frame ( $n$ ) from the base frame ( $0$ )