Planar Mechanics

Planar Mechanics, also called 2D Kinematics, Planar Mechanism Analysis, or Two-Dimensional Machine Design, is the branch of engineering that studies motion and force transmission in planar mechanical systems. This fundamental discipline provides the analytical foundation for designing precise, reliable mechatronic systems from robotic arms and manufacturing equipment to automated machinery and automotive components.

This course explores how mechanical systems move and transmit forces in two-dimensional space—knowledge essential for designing sophisticated mechatronic systems that require controlled motion, precise positioning, and optimized force transmission.

Lesson Structure & Approach

Each lesson follows our systems-based pedagogical approach:

1. 🔧 Real-World System Problem Begin with complete mechatronic systems (robotic arms, manufacturing equipment, automotive systems) facing specific kinematic and dynamic challenges.

2. 📚 Fundamental Theory Develop the mathematical and kinematic principles needed to analyze and solve the planar motion problem.

3. 🎯 System Application Apply theory to the original system with step-by-step kinematic solutions and design verification.

4. 🛠️ Design Guidelines Extract practical rules and best practices for professional planar mechanism design.

Learning Path

1. Build Kinematic Foundations Master joint analysis and degrees of freedom that form the basis for all planar mechanism design.

2. Understand Position Relationships Learn geometric constraints and position analysis for complex linkage systems.

3. Apply Motion Analysis Use velocity and acceleration analysis methods for dynamic system optimization.

4. Design Real Systems Apply planar mechanics principles to advanced mechatronic challenges including cam systems and force optimization.

Course Structure

This course is organized around recurring mechatronic systems for coherent knowledge building:

• Foundation & Analysis
• Dynamics & Synthesis

1. Kinematic Joints and Constraint Analysis

   Master joint types and degrees of freedom through modular robotic arm design, covering Grübler’s equation and joint selection guidelines.

2. Position Analysis of Planar Linkages

   Learn vector loop equations and geometric constraints through four-bar linkage suspension system optimization.

3. Velocity Analysis and Instantaneous Centers

   Explore velocity polygons and relative motion in crank-slider engine/compressor mechanisms.

Primary Focus Systems

Throughout this course, we analyze five core mechatronic systems from multiple perspectives:

Why Planar Mechanics Matters for Mechatronics

Expected Learning Outcomes

By completing this course, students will be able to:

1. Analyze any planar mechanism for position, velocity, and acceleration behavior
2. Design mechanisms for specific motion requirements and performance criteria
3. Optimize mechanism geometry for force transmission and dynamic performance
4. Select appropriate mechanisms for diverse mechatronic applications
5. Integrate kinematic analysis with motor sizing and control system design

Interactive Learning Tools

Each lesson includes specialized interactive components:

• Joint DOF Calculator - Real-time constraint analysis
• Four-Bar Position Visualizer - Geometric relationship explorer
• Crank-Slider Velocity Animator - Motion profile visualization
• Geneva Mechanism Plotter - Acceleration curve analysis
• Cam Profile Designer - Motion programming tool
• Robot Force Calculator - Integrated system analysis

Prerequisites

Vector mechanics, basic calculus, and elementary physics concepts. Familiarity with engineering graphics and coordinate systems recommended.

Key Resources

• Textbooks: “Theory of Machines and Mechanisms” (Uicker, Pennock & Shigley), “Kinematics and Dynamics of Machinery” (Wilson & Sadler)
• Software: MATLAB/Simulink, SolidWorks Motion, Working Model
• Standards: ASME, ISO mechanism design standards

Ready to begin? Navigate to the first lesson to start your journey into planar mechanics!