GSOC'25: Expanding Actuator and Force Modelling Capabilities in physics.mechanics Module

[Pratyksh Gupta]

Hello SymPy developers, 

I am Pratyksh Gupta, a student at IIT Patna pursuing a Bachelor’s in Computer Science and Data Analytics. I am an enthusiast of physics and an active contributor to sympy. Recently, I came across the idea of enhancing the actuator capabilities in sympy’s physics.mechanics module, which aligns with my interest in symbolic mechanics and control systems.

Proposed Enhancements:

I have proposed a structured enhancement and improvement plan divided into multiple phases:

Phase 1: Completing Hwayeon Kang’s Future Work (90 hours) : -

This phase aims to finish pending work from the GSoC 2024 contributions to ensure continuity and build upon existing momentum.
• Friction Example Model (Sliding Block on Rotating Disc):
The current implementation needs to be completed by merging PR #26936 (if not already merged) and resolving any remaining issues from issue #26929. This will provide a clear, well-documented example of how frictional forces act in rotational motion scenarios.
• Hill’s Muscle Model Actuator:
The HillTypeMuscle actuator (PR #26443) will be finalised by addressing any remaining bugs and ensuring seamless integration with the PathwayBase system, which is essential for biomechanics applications.
• Example Model for Hill’s Muscle Actuator:
A simple example of a muscle-actuated joint will be developed, showcasing how muscle forces generate motion. A tutorial will also be provided to help users simulate muscle behaviour using sympy’s numerical solvers.

Phase 2: Expanding Nonlinear Springs and Dampers (175 hours) : -

This phase focuses on introducing more advanced actuator models to capture real-world behaviours.
• Polynomial Spring:
A PolynomialSpring model will allow defining force-displacement relationships using polynomials (F = -∑ kᵢ xⁱ). This is useful for modelling materials with nonlinear stiffness properties.
• Piecewise Linear Spring:
A PiecewiseLinearSpring model will introduce different linear segments for force response, which is essential for capturing non-uniform stiffness characteristics in engineering structures.
• Nonlinear Damper:
This model will allow damping force to be defined as a nonlinear function of velocity (F_damping = -damping_coefficient * f(velocity)), making it more accurate for fluid and viscoelastic damping applications.
• Bouc-Wen Hysteresis Model:
A key enhancement for capturing energy dissipation in structural systems, this model represents hysteretic behavior commonly found in materials undergoing cyclic loading, such as rubber, steel under plastic deformation, and seismic dampers.

Phase 3: Integration and Advanced Musculotendon Dynamics (350 hours) : -

This phase aims to extend musculotendon dynamics and incorporate viscoelastic models for realistic simulations.
• Maxwell Viscoelastic Model:
this model represents a spring and damper in series, commonly used for modelling viscoelastic materials. It helps simulate realistic time dependent deformation in biological tissues and polymers.
• Fiber Length State (Damped Elastic Tendon):
this enhancement accounts for the elasticity and damping of the tendon, which affects how muscle force is transmitted to bones. By introducing tendon_length as a dynamic variable, it provides a more realistic representation of muscle-tendon dynamics.
• Tendon Force State (Damped Elastic Tendon):
this feature models tendon force as a state variable, capturing both elastic and damping effects (F_t = k_e * (l_t - l₀) + k_v * ṡ(l_t)). This helps simulate the time-dependent response of tendons under varying loads.


Extended Phase: Integration with Control Systems (Additional Feature) : -

Integration with Control Systems : -
• develop interfaces to integrate the enhanced actuator models with control systems like PID controllers and state feedback controllers.
• provide practical examples showcasing how these controllers can be used to regulate forces and motions in mechanical and robotic systems.
• this will bridge gap between symbolic modelling and real time control, making sympy useful for engineers and researchers working on dynamic system control.

I would appreciate insights on the feasibility of this approach and any potential challenges or key areas of focus that I should consider and any refinement that i have to make in this proposed enhancement and improvements.

Looking forward to your thoughts!

Best Regards,
Pratyksh Gupta

[Jason Moore]

Dear Pratyksh,

I would suggest just focusing on improving the variety and capabilities of our muscle force models, starting with Hill's original model. That is plenty for the scope of the different size projects. Once you implement Hill's model (90 hours), then you could add more features to muscles or do another muscle model.

Jason

moorepants.info
+01 530-601-9791

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[Pratyksh Gupta]

Hi Jason,

I have proposed a refined structured enhancement and improvement plan divided into multiple phases:

Refined Proposed Enhancements:

Phase 1 (90 hours) : -

• Friction Example Model (Sliding Block on Rotating Disc):
The current implementation needs to be completed by merging PR #26936 (if not already merged) and resolving any remaining issues from issue #26929. This will provide a clear, well-documented example of how frictional forces act in rotational motion scenarios.
• Hill’s Muscle Model Actuator:
The HillTypeMuscle actuator (PR #26443) will be finalised by addressing any remaining bugs and ensuring seamless integration with the PathwayBase system, which is essential for biomechanics applications.
• Example Model for Hill’s Muscle Actuator:
A simple example of a muscle-actuated joint will be developed, showcasing how muscle forces generate motion. A tutorial will also be provided to help users simulate muscle behaviour using sympy’s numerical solvers.

Phase 2 (175 hours) : -

• Fiber Length State (Damped Elastic Tendon):
this enhancement accounts for the elasticity and damping of the tendon, which affects how muscle force is transmitted to bones. By introducing tendon_length as a dynamic variable, it provides a more realistic representation of muscle-tendon dynamics.
• Tendon Force State (Damped Elastic Tendon):
this feature models tendon force as a state variable, capturing both elastic and damping effects (F_t = k_e * (l_t - l₀) + k_v * ṡ(l_t)). This helps simulate the time-dependent response of tendons under varying loads.

• Nonlinear Damper:
this model will allow damping force to be defined as a nonlinear function of velocity (F_damping = -damping_coefficient * f(velocity)), making it more accurate for fluid and viscoelastic damping applications.

Phase 3 (350 hours) : -
• Bouc-Wen Hysteresis Model:
A key enhancement for capturing energy dissipation in structural systems, this model represents hysteretic behaviour commonly found in materials undergoing cyclic loading, such as rubber, steel under plastic deformation, and seismic dampers.

Extended Phase (Additional Feature) : -

• Maxwell Viscoelastic Model:
this model represents a spring and damper in series, commonly used for modelling viscoelastic materials. It helps simulate realistic time dependent deformation in biological tissues and polymers.

I would appreciate insights on any potential challenges or key areas of focus that I should consider and any refinement that i have to make in this refined proposed enhancement and improvements.

Looking forward to your thoughts!

Regards,
Pratyksh Gupta

[Hwayeon Kang]

Hi Pratyksh,

I'd recommend focusing on Hills model -- the parts you've referred to as "Hills muscle model actuator", "example model for hills muscle actuator", "fiber length state", and "tendon force state" in your proposal. Given the time constraints, it's difficult to complete everything listed, and hills model alone is a substantial and complex topic. Once you begin working through the actual implementation, you'll find it quite challenging and time-consuming. So I'd advise narrowing your scope to hills model and start thinking concretely about how you plan to implement it. At the moment, I don't see any technical or theoretical details or a clear plan in your proposal.

Hwayeon

[Pratyksh Gupta]

Hello Hwayeon,

I have completed my proposal and here is the link of the document, please review this and give suggestions on this proposal on Extending Classical Mechanics Module: Implementing Specific Forces and Torques.

Proposal Link : https://docs.google.com/document/d/1kBhidN3FIFkJ_-M2aQn-KA64cg_kDq-TqRYZTSf3P8U/edit?usp=sharing

Regards,
Pratyksh

On Friday, April 4, 2025 at 10:23:28 PM UTC+5:30 Pratyksh Gupta wrote:

Hello Hwayeon,

I have completed my proposal and here is the link of the document, please review this and give suggestions on this proposal on Extending Classical Mechanics Module: Implementing Specific Forces and Torques.

Proposal Link : https://docs.google.com/document/d/1kBhidN3FIFkJ_-M2aQn-KA64cg_kDq-TqRYZTSf3P8U/edit?tab=t.0

Regards,
Pratyksh