MODULE M1 · 10.0 HOURS

Fundamentals of Robot Kinematics

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LEARNING OBJECTIVES

Module objectives

  1. Understand the basic definitions of robot kinematics and the concept of rigid-body transformation.
  2. Learn how to mathematically describe the position and orientation of a robot using coordinate system transformations and rotation matrices.
  3. Acquire basic kinematic theories for designing an 5-finger robotic hand and learn analytical approaches.

Fundamentals of Robot Kinematics

Robot kinematics is the study of robot motion in terms of position, velocity, and acceleration without considering forces or torques [S1]. The starting point for designing a manipulator, such as a robotic hand, is to describe the state of each joint as coordinates in space.

1. Rigid-body Transformation

Each link of a robot is considered a rigid body, and the transformation from one coordinate system to another is represented as a combination of rotation and translation. In 3-dimensional space, the rotation matrix $R$ is an orthogonal matrix, through which the orientation between two coordinate systems is defined [S1].

2. Forward Kinematics

Forward kinematics is the process of calculating the position and orientation of the end-effector when the joint variables (angles or positions) are known. For an 5-finger robotic hand, the position of the fingertips is obtained through the finger joint angles ($\theta_1, \theta_2, \dots, \theta_n$).

3. Inverse Kinematics

Inverse kinematics is the process of finding the joint variables required to achieve a desired fingertip position. It consists of non-linear equations, and solutions may not exist or multiple solutions may occur [S1].

WORKED EXAMPLES

Worked examples

  1. Example 1: Find the end position $(x, y)$ of a robot link with 1 rotation joints in a 2-dimensional plane. When the joint angle is $\theta$ and link length is $L$, $x = L \cos(\theta)$ and $y = L \sin(\theta)$ [S1].
  2. Example 2: Describe a 2-dimensional rotation matrix $R$ that rotates by $\theta$ about the $x$-axis. $R = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) \\ \cos(\theta) \end{bmatrix}$ [S1].

LAB PROTOCOL

Coordinate System Transformation Simulation and Basic Kinematic Analysis

  1. 1

    Create an 2-link planar manipulator model using kinematic analysis software.

  2. 2

    Observe the trajectory of the end position while changing the joint angles.

  3. 3

    Derive inverse kinematic equations manually and compare them with the simulation results.

Safety check
  • Adjust screen brightness and take periodic breaks when working on computers.
  • This practice is simulation-based, so hardware energization is not required.

Lab deliverables

  • Summary report including the kinematic analysis process
  • Trajectory simulation result images

ASSIGNMENT

Kinematic Modeling of 5-Finger Robotic Hand Joint Structure

Deliverables

Rubric

  • Mathematical accuracy of rotation matrices
  • Physical validity of forward kinematics equations
  • Logical structure of the report

KNOWLEDGE CHECK

Knowledge check

1What is the discipline in robot kinematics that describes only motion without considering forces or torques?
2In 3-dimensional space, what matrix defines the orientation between two coordinate systems?

FIELD CHECK

Completion criteria

  • Completion of theory lectures
  • Submission of kinematic analysis result report
  • Achieve 100 points on the theory quiz

MODULE SOURCES

Module sources

  1. Introduction to Robotics: Mechanics and Control - John J ... John J.Craig-Introduction to Robotics Mechanics and Control ... Introduction to robotics : mechanics and control : Craig ... Introduction to Robotics: Mechanics and Control (3rd Edition) Introduction to robotics : mechanics and control : Craig ... Introduction to Robotics: Mechanics and Control - John J ...books.google.com · textbook