Robot Kinematics Study Notes

Introduction to Robot Kinematics

The study of robot kinematics involves understanding how robotic devices move, their structures, and the geometrical relationships of their components. This document outlines fundamental concepts, definitions, joint types, and kinematic principles vital to the field of robotics.

Definition of a Robot

A robot can be defined as a re-programmable, multi-functional manipulator designed to move material, parts, tools, or specialized devices through variable programmed motions to perform a variety of tasks.

Functions of Robots

Robots have several functions that enhance their capabilities:

• Generate angles of rotation of joints: Robots can adjust the angles at which their joints rotate, allowing for precise movements.

• Integrate tooling and sensors: They can utilize various tools and sensors to perform tasks more effectively.

• Decide the most suitable path: Robots can assess different potential paths to select the most efficient route for task execution.

• Repetitive moves: They can perform the same series of movements consistently.

• Memory capabilities: Robots can memorize tasks and processes.

The 3 main functions of a robot can be categorized as follows:

1. Sense: This involves using sensors and limit switches to gather data about the environment.

2. Think/Correlate/Analyze: This is achieved through the use of computers, microcontrollers, and programmable logic controllers (PLCs).

3. Act: This refers to the movements executed by arms, links, and end effectors.

Kinematics of Robots

What is Kinematics?

Kinematics is the branch of physics that deals with the motion of objects and can be defined in the context of robotics as the science of motion of robots, focusing on their positions, velocities, and accelerations. It analyses the relationship among these parameters within robotic systems.

Application of Geometry in Kinematics

Robot kinematics applies geometric principles to the study of the movement of multi-degree-of-freedom (DOF) kinematic chains that compose robotic structures. In this context, the robot's links are modeled as rigid bodies, and its joints provide pure rotation or translation.

Kinematic Relationships

Robot kinematics investigates relationships between the dimensions and connectivity of kinematic chains, the positional, velocity, and acceleration data of the links in a robot system to facilitate the planning and control of movements, as well as compute the necessary actuator forces and torques.
Additionally, the study of robot dynamics includes analyzing the relationship between mass and inertia properties, motion, and associated forces and torques.

Joint Types in Robots

Robots depend heavily on joints that provide varying degrees of motion:

• Revolute Joint: Offers 1 degree of freedom (1 DOF) characterized by a rotational variable (angle θ).

• Prismatic Joint: Provides linear movement (to and fro) and features a variable distance (d).

• Spherical Joint: Commands 3 degrees of freedom, involving three rotational angles (θ1, θ2, θ3), allowing for multidirectional movement.

Anatomy of a Robot: Joints

Each joint in a robot connects two links: an input link and an output link, offering controlled relative movement. The rigidity of robotic links indicates how they are designed and connected. Most robots rest on stationary bases like floors, with each joint being numbered for consistency (e.g., link-0, joint-1, link-1, etc.).

Types of Joints Explained

1. Linear Joint (Type L Joint): Provides translational sliding motion with parallel axes between the input and output links.

2. Orthogonal Joint (Type U Joint): Exhibits translational sliding motion but with perpendicular axes between the two links.

3. Rotational Joint (Type R Joint): Offers rotational movement with axes perpendicular to those of the input and output links.

4. Twisting Joint (Type T Joint): Involves rotary motion where the rotation axis is parallel to the links.

5. Revolving Joint (Type V Joint): Features parallel input axes and perpendicular output axes.

Robot Configurations

Selective Compliance Assembly Robot Arm (SCARA)

Robot configurations take different forms based on their joints and design:

• Polar Configuration: Incorporates a sliding arm that rotates around both vertical and horizontal axes, facilitated by a combination of L-joints and T-joints.

• Cylindrical Configuration: Characterized by a vertical column, allows movement of an arm assembly up/down, in/out relative to the column's axis, often using L-joints and O-joints.

• Cartesian Coordinate Robot: Also known as a rectilinear robot, it has three sliding joints that operate in an orthogonal manner.

• Jointed-Arm Robot (Articulated): Mimics human arm movement with a vertical column that swivels and various joints located at strategic points (e.g., shoulder and elbow).

Work Space of a Robot

The workspace of a robot refers to the set of all locations that the robot’s end effector can reach. Understanding a robot's workspace is crucial for task performance as it defines the areas where movements and tasks can be executed effectively.

Degrees of Freedom (D.O.F) in Robotics

Degrees of freedom represent the number of independent motions a robot or mechanism can perform. A rigid body has 6 D.O.F in 3D space, but constraints from joints and links can reduce available D.O.F. Therefore, the relationship can inform the required D.O.F necessary for particular tasks.

Degrees of Freedom in the Human Arm

The human arm exemplifies complex D.O.F:

• Shoulder: 3 D.O.F (pitch, roll, yaw)

• Elbow: 1 D.O.F

• Wrist: 3 D.O.F (pitch, roll, yaw)
  This totals to 7 D.O.F for a human arm, illustrating significant flexibility in motion.

Specific Examples of Robotic Designs

PUMA 560 Robot

The PUMA 560 robot features six revolute joints resulting in a 6 D.O.F configuration:

• Joint angles:

  • Waist: 320° (Joint 1)

  • Shoulder: 250° (Joint 2)

  • Elbow: 270° (Joint 3)

  • Wrist Rotation: 300° (Joint 4)

  • Wrist Bend: 200° (Joint 5)

  • Flange: 532° (Joint 6)

Forward Kinematics

Forward kinematics deals with determining the position of the robot's end effector given joint angles and the lengths of the links. It typically involves equations where:
$ext{Position} = f(d<em>1, d</em>2, heta<em>1, heta</em>2)$
Where you start with known distances and angles to find the coordinates of the final point.

Inverse Kinematics

Inverse kinematics addresses the problem of determining the necessary joint angles to achieve a specific position of the robot’s end effector. It can be expressed as:
$ext{Angles} = g( ext{Destination Point})$
Where the end goal is to calculate the necessary angles to reach a known destination.

Importance of Reference Frames

Reference frames are crucial in robot kinematics as they define positions relative to various components. By establishing specific reference points, you can determine motion and positioning accurately. For instance, to understand the positioning of the robot's various parts concerning a product, all components must be analyzed within a unified reference frame.