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Related Concept Videos

Constraints and Statical Determinacy01:26

Constraints and Statical Determinacy

In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...
Support Reactions in Three Dimensions01:27

Support Reactions in Three Dimensions

Support reactions in three dimensions help maintain the stability and equilibrium of various structures and systems. These reactions prevent the system from translating and rotating, ensuring the design can withstand external forces and perform its intended function efficiently and safely. Some of the supports providing support reactions in three dimensions are discussed below:
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Virtual Work for a System of Connected Rigid Bodies01:06

Virtual Work for a System of Connected Rigid Bodies

Virtual work is a powerful method used to solve problems involving several connected rigid bodies. When the system is in equilibrium, virtual work is zero. This allows the calculation of the resulting forces when a system undergoes a virtual displacement. When attempting to analyze such a system, first, use a free-body diagram, where an independent coordinate represents the configuration of the links, and mark its deflected position resulting from the positive virtual displacement.
Next,...
One-Degree-of-Freedom System01:24

One-Degree-of-Freedom System

In mechanical engineering, one-degree-of-freedom systems form the basis of a wide range of electrical and mechanical components. Using these models, engineers can predict the behavior of various parts in a larger system, which gives them insight into how different forces interact with each other.
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...
Lagrange Multipliers: One Constraint01:29

Lagrange Multipliers: One Constraint

In constrained optimization, the objective is to maximize or minimize a quantity while satisfying a fixed condition. A standard example is a rectangular pen built against a barn wall using 100 meters of fencing. Because the wall provides one side of the enclosure, only the other three sides require fencing. The problem is to find the dimensions that produce the greatest possible area.Let L represent the length parallel to the wall and W the width perpendicular to it. The area of the pen is A =...
Lagrange Multipliers: Two Constraints01:28

Lagrange Multipliers: Two Constraints

The method of Lagrange multipliers with two constraints is used to optimize a function subject to two independent constraints. In many applications, the objective function represents a quantity to be maximized or minimized, such as cost, area, distance, or energy. The two constraints represent requirements that the solution must satisfy, such as fixed volume, limited resources, or prescribed dimensions.For a function of three variables, each constraint forms a surface in three-dimensional space.

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Related Experiment Video

Updated: Jun 13, 2026

Design and Fabrication of an Elastomeric Unit for Soft Modular Robots in Minimally Invasive Surgery
11:06

Design and Fabrication of an Elastomeric Unit for Soft Modular Robots in Minimally Invasive Surgery

Published on: November 14, 2015

Dynamic active constraints for hyper-redundant flexible robots.

Ka-Wai Kwok1, George P Mylonas, Loi Wah Sun

  • 1Royal Society/Wolfson Medical Image Computing Laboratory, Institute of Biomedical Engineering, Imperial College London, London, United Kingdom. k.kwok07@imperial.ac.uk

Medical Image Computing and Computer-Assisted Intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention
|April 30, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces dynamic active constraints for robot-assisted heart surgery, improving navigation accuracy during pulmonary vein isolation. The new method enhances surgical precision for treating atrial fibrillation.

Related Experiment Videos

Last Updated: Jun 13, 2026

Design and Fabrication of an Elastomeric Unit for Soft Modular Robots in Minimally Invasive Surgery
11:06

Design and Fabrication of an Elastomeric Unit for Soft Modular Robots in Minimally Invasive Surgery

Published on: November 14, 2015

Area of Science:

  • Medical Robotics
  • Surgical Navigation
  • Computational Anatomy

Background:

  • Robot-assisted surgery enhances surgeon capabilities via navigation guidance.
  • Virtual fixtures and active constraints are key navigation tools.
  • Cardiac procedures require precise instrument control amidst dynamic anatomical changes.

Purpose of the Study:

  • To present a real-time modeling scheme for dynamic active constraints.
  • To enable fast and simple mesh adaptation for cardiac deformation.
  • To guide flexible robots for procedures like pulmonary vein isolation.

Main Methods:

  • Developed a real-time modeling scheme for dynamic active constraints.
  • Implemented fast and simple mesh adaptation for cardiac deformation.
  • Constructed a smooth tubular pathway for robot navigation around the heart.
  • Incorporated detailed geometrical constraints for the entire surgical instrument, including forbidden regions.

Main Results:

  • Demonstrated a real-time modeling scheme for dynamic active constraints.
  • Achieved fast and simple mesh adaptation under cardiac deformation.
  • Successfully guided a flexible hyper-redundant robot for pulmonary vein isolation.
  • Experimental validation confirmed the speed and accuracy of instrument navigation with dynamic constraints.

Conclusions:

  • The proposed dynamic active constraints enhance real-time navigation in robot-assisted cardiac surgery.
  • The method accurately guides surgical instruments, even with complex anatomical changes.
  • This approach offers improved precision for procedures like pulmonary vein isolation in treating atrial fibrillation.