Modeling Leonardo’s Paddleboat with SIMPACK

Model created by Dassault Systemes

Introduction: From Renaissance Ingenuity to Modern Engineering 

Leonardo da Vinci’s 15th-century paddleboat was a marvel of its time, combining elegant biomimicry and mechanical innovation. Innovation is a concept that transcends time and technological boundaries. Leonardo da Vinci, a polymath of the Renaissance period, embodied this very spirit through his contributions to art, science, and engineering. His use of cogwheels to boost rowing efficiency, coupled with hull designs inspired by fish, showcased an early grasp of dynamics that modern engineers now simulate virtually. 

Today, engineering tools like SIMPACK allow us to reimagine da Vinci’s vision in high fidelity. This blog explores how SIMPACK’s nonlinear flexible body capabilities bring historical innovation to life through advanced multibody dynamics. 

Reconstructing the Paddleboat in SIMPACK 

To study the dynamics of da Vinci’s paddleboat, a detailed CAD model was imported into SIMPACK using the “Power By” connector from the 3DEXPERIENCE platform. This connector ensured a smooth transition from geometry to simulation, preserving existing joints, bodies, and constraints directly within SIMPACK. This seamless integration accelerates the setup process and maintains the fidelity of the original design. 

Once imported, engineers focused on the rope-based transmission system ,  the heart of the pedal-driven mechanism. While rigid body modeling could approximate the motion, capturing the nuanced, real-world behavior of the rope under tension and motion required a flexible body approach. 

Model created by Dassault Systemes

The Challenge: Modeling Rope Dynamics Accurately 

The rope connects the pedal mechanism to a central driving wheel, experiencing both axial and bending loads as it wraps around pulleys and transfers force. This motion is inherently nonlinear and dynamic, affected by factors like stretching, slack, vibration, and contact forces. 

To simulate this accurately, the engineering team used SIMBEAM, SIMPACK’s flexible body module designed for modeling 3D beam-like structures in mechanical systems. 

SIMBEAM: Realistic Nonlinear Flexible Body Simulation 

The rope in the simulation was modeled as a non-linear flexible body using SIMBEAM, which allows for the creation of three-dimensional flexible beam structures. SIMBEAM supports two modeling approaches: 

• Modally reduced FEM ,  ideal for general flexible structures using precomputed modes 

• Nonlinear finite difference method ,  optimal for large deformations and transient dynamic effects 

For this case, the finite difference method was chosen due to its superior performance in capturing rope elongation, bending, and real-time shape adaptation under load. 

Model created by Dassault Systemes.

Rayleigh Damping and Energy Loss 

The model also incorporated Rayleigh damping, which accounts for energy dissipation through proportional mass and stiffness damping terms. This allowed for more realistic modeling of how the rope resists oscillation and settles into steady-state motion ,  key for analyzing system stability and load feedback. 

Visualizing the Simulation 

Although not shown here, SIMPACK allows engineers to generate: 

• Time history plots of tension or displacement at key rope nodes 

• Animations of the full-body dynamics and flexible deformations 

• Overlay comparisons of design alternatives based on physical performance 

Such visual tools aid validation and communication across engineering teams, especially when optimizing real-world prototypes. 

Why SIMPACK and not Just Abaqus? 

While Abaqus excels at detailed stress and strain analysis, SIMPACK is built for system-level multibody dynamics. It shines when: 

• Components interact through joints and motion constraints 

• Flexible and rigid parts coexist within time-domain simulations 

• Engineers require fast, real-time iteration for mechanism behavior 

In essence, SIMPACK is ideal for motion-centric studies, while Abaqus focuses on structural stress and fatigue ,  making them complementary in workflows. 

Key Advantages of SIMPACK for Flexible Body Systems 

SIMPACK delivers significant benefits for teams modeling complex mechanisms like da Vinci’s paddleboat: 

• No finite element mesh needed – flexible bodies are modeled directly, saving time 

• Rapid simulations – full-system runs completed in minutes rather than hours 

• High fidelity – nonlinear response captured realistically under real-world conditions 

• Iteration-friendly – supports fast evaluation of geometry, material, or damping changes 

• Scalable – handles full system simulations with multiple flexible and rigid parts 

Design Iteration: A Practical Example 

Consider evaluating three alternative rope configurations: 

• Different cross-sectional materials (e.g., steel vs. synthetic fiber) 

• Varying tension preload values 

• Alternate pulley layouts 

With SIMPACK, all three scenarios can be evaluated rapidly, producing response data for comparison ,  such as rotational lag at the output shaft, or oscillation amplitude after load application. These insights enable early-stage design decisions that would be too slow or costly using conventional FEA alone. 

Conclusion: Simulating the Future with Tools of the Past 

Leonardo da Vinci imagined mechanisms that were centuries ahead of his time. Today, SIMPACK gives us the power to simulate those mechanisms with mathematical rigor and system-level fidelity. Whether you're analyzing pedal-driven propulsion or validating a next-gen transmission system, SIMPACK empowers engineers to model the real world, flexibility, friction, and all. 

By embracing flexible body dynamics in concept design and virtual prototyping, engineers can prevent costly mistakes, increase confidence in system behavior, and build smarter, faster machines ,  all while drawing inspiration from history’s greatest inventors. Just as Leonardo da Vinci’s innovative designs reshaped the world of transportation in his time, modern simulation tools like SIMPACK are revolutionizing the way we approach mechanical system design today. 

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