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kinematics

The branch of mechanics that describes motion without considering the forces that cause it. In robotics, it focuses on how joints and links move in space—essentially the geometry of motion. Think of it as describing where a robot moves and how, but not why or how hard it has to push.


The Basics

Kinematics is the mathematical study of motion without worrying about forces. It answers: Where will the robot move? How fast? What path will it follow?—but not Why or What forces are needed?

Key Principle

Kinematics focuses on:

  1. Position (where things are)
  2. Velocity (how fast they move)
  3. Acceleration (how quickly speed changes)
  4. Orientation (which way things point)

Kinematics ignores:

  1. Forces and torques
  2. Motor power
  3. Energy consumption
  4. Material strength
Motion Description ← Kinematics
     ↓
Forces Needed ← Dynamics (separate topic)

Forward vs. Inverse Kinematics

Forward Kinematics (FK)

Given joint angles → Calculate end-effector position

Joint 1: 45°
Joint 2: 30°  } → Where is the gripper?
Joint 3: 60°

Used for: Predicting where the arm ends up

Inverse Kinematics (IK)

Given desired end-effector position → Calculate required joint angles

Gripper at (x=0.5m, y=0.3m, z=0.8m)  } → What angles needed?
Orientation: pointing down

Used for: Planning how to reach a target

Real-World Robot Example

Pick-and-place task:

  1. Target location: Box at position (x, y, z)
  2. Inverse kinematics: Calculate joint angles needed
  3. Forward kinematics: Verify the arm reaches exactly there
  4. Execute: Move joints to those angles
  5. Result: Gripper precisely positioned

Key Concepts in Robotics Kinematics

Concept

Definition

Degrees of Freedom (DOF)

Number of independent joints that control motion

Workspace

All positions the robot can physically reach

Singularity

Position where the robot loses control in some direction

Jacobian Matrix

Mathematical tool relating joint speeds to end-effector speed

Why Kinematics Matters

Essential for:

  1. Motion planning - calculating paths from A to B
  2. Trajectory control - smooth, coordinated movement
  3. Collision avoidance - predicting where arm goes
  4. Reach analysis - determining what the robot can access
  5. Real-time control - fast calculations for immediate response

Practical Applications

Manufacturing robot:

  1. Kinematics calculates joint angles to reach each workstation
  2. Ensures precise part placement
  3. Optimizes cycle time

Collaborative robot:

  1. Kinematics predicts arm position for safety zones
  2. Ensures smooth, human-like motion
  3. Enables intuitive teaching

Mobile robot arm:

  1. Kinematics accounts for base position + arm angles
  2. Calculates reach in complex environments
  3. Plans navigation and manipulation simultaneously

Kinematics vs. Dynamics

Aspect

Kinematics

Dynamics

Focus

Motion description

Forces & acceleration

Question

Where and how fast?

What force is needed?

Example

Joint angle → position

Motor torque required

Complexity

Geometry-based

Physics-based

Simple Analogy

Kinematics = GPS navigation

  1. Tells you where you'll go and how fast
  2. Doesn't care about engine power

Dynamics = Engine specifications

  1. Tells you what force/power is needed
  2. Based on kinematics predictions

Key Takeaway

Kinematics is the "language of robot motion"—it provides the mathematical framework to describe and predict where a robot moves, how it gets there, and what path it follows. It's the foundation for all robot control, from simple positioning to complex manipulation tasks.

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Contents The Basics Key Principle Forward vs. Inverse Kinematics Real-World Robot Example Key Concepts in Robotics Kinematics Why Kinematics Matters Practical Applications Kinematics vs. Dynamics Simple Analogy Key Takeaway