Page 64 - Toucpad robotics C11

Cranes and Excavator Arms
Description: The arm of a large crane or an excavator is a spatial mechanism. It’s designed to lift and move heavy
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loads across large distances and in various directions.
How it Works: The mechanism typically consists of a large base that can rotate (yaw), a long boom that can be
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raised and lowered (pitch), and a hydraulic system that extends and retracts the arm. The combination of these
movements allows the crane to reach objects in any part of a construction site and place them with precision. The
entire system operates in three-dimensional space, accounting for gravity, load, and wind.

Spatial mechanisms are crucial for any application where motion is not restricted to a flat plane. Their design requires
a deep understanding of three-dimensional kinematics and dynamics, which is a core part of advanced robotics and
mechanical engineering. They are the systems that allow robots to truly interact with our three-dimensional world,
performing tasks that require the full range of motion.

Robot Kinematics: The Geometry of Motion

Planar Open-Chain Mechanism
A Planar Open-chain Mechanism is a series of rigid links connected by joints, where the entire structure is confined to
moving within a single, two-dimensional plane. It’s called “open-chain” because the links are arranged in a sequence,
from a fixed base to a final end-effector, without forming any closed loops. This type of mechanism is a great starting point
for understanding kinematics because its motion can be described using straightforward two-dimensional geometry and
trigonometry.

Components
Links: Rigid rods of a specific length.
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Joints: Connections between the links that allow relative motion. In planar mechanisms, these are typically
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revolute (R) joints (allowing rotation) or prismatic (P) joints (allowing linear sliding).
Base: A fixed link that acts as the starting point.
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End-Effector: The final link, to which a tool or gripper is attached.
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The “planar” part means that all joint axes are parallel to each other and perpendicular to the plane of motion, so the
entire arm stays flat.
Forward Kinematics of Different Planar Configurations

Forward kinematics is the process of calculating the position and orientation of the robot’s end-effector in a fixed
reference frame, given the known lengths of all the links and the values of all the joint variables (e.g., joint angles for
revolute joints or joint displacements for prismatic joints).

Let’s examine two common planar open-chain configurations.
Configuration 1: The 2R Planar Manipulator

The “2R” configuration refers to a planar manipulator with two revolute joints.

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Touchpad Robotics - XI