10.1.2. Kinematic Chains

Kinematic Chains: Interconnection of rigid bodies (links) and joints to form a manipulator.

A kinematic chain is essentially a series of rigid bodies (called links) connected by joints that allow relative motion between them. In robotic terms, these connections allow for the creation of manipulators that can perform complex tasks by moving in coordinated ways. Each joint connects two links and can allow different types of motion - either rotating (revolute) or sliding (prismatic).

Imagine a puppet controlled by strings. Each of the strings represents a joint, and the puppet's limbs represent the links. Just like a puppeteer can move the puppet's joints to make it perform actions, in a robot, the kinematic chain enables the robot to perform tasks by moving its limbs.

Rigid bodies (links) connected by joints to form a manipulator.

The links in a kinematic chain are the actual physical structures that make up a robot's arm or body. They are rigid, meaning they maintain their shape and do not bend or deform under loads. The way these links are assembled and connected through joints determines the robot's overall functionality and how it can move in its environment.

Think of a bicycle. The metal parts of the frame are rigid links that maintain their shape, while the pedals and handlebars are connected to the frame with joints – allowing for movement. Just as a bicycle moves through coordination of its parts, a robot moves through its links and joints.

Types of Joints: Revolute (Rotational), Prismatic (Translational).

In a kinematic chain, the joints play a crucial role in defining how the links move. There are two primary types of joints: revolute joints, which allow rotational movement (like a door hinge), and prismatic joints, which allow translational movement (like a drawer sliding open). These types of joints give robots their flexibility of movement, enabling them to manipulate their environment effectively.

Consider an arm. Your shoulder acts like a revolute joint allowing your arm to rotate around it, while your elbow can be thought of as a prismatic joint, allowing your forearm to slide out and in. Just like your arm, robots use these kinds of joints to achieve complex motions.

Kinematic Parameters: Joint angles (θ) for revolute joints; Joint displacements (d) for prismatic joints.

Kinematic parameters are the variables that describe the configuration of the robot at any given time. For revolute joints, these parameters are measured as angles (θ), which tell us how much the joint has rotated. For prismatic joints, the displacement (d) measures the linear distance the joint has moved. These parameters are essential for calculating the robot's position and orientation in space.

Think of driving a car. The steering wheel's angle (like the joint angle θ) tells you how much you are turning, while the position of the gear shift (like joint displacement d) tells you whether you are accelerating or reversing. Similarly, the kinematic parameters provide critical information on a robot's movement.

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