| Week | Dates Topics | Notes | Codes, etc. |
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Module 1: Principles and Concepts | ||
| 1 | Jan. 4, 2024: The spirit of compliant mechanisms: an overview of compliant mechanisms and their applications. |
Prof. Ashok Midha's thoughts on compliant mechanisms and mechanisms in general Overview of compliant mechanisms Spirit of compliant design Applications of compliant mechanisms |
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| 2 |
Jan. 9, 2024:
Introducing Matlab and COMSOL finite element software to analyze compliant mechanisms. Familiarization with beam finite element codes in Matlab (linear and nonlinear) Jan. 11, 2024: In-class hands-on practice with Matlab and COMSOL to understand how compliant mechanisms work. | Subtleties in using finite element analysis of compliant mechanisms. |
Matalb code linear finite element analysis with beams Matalb code geometrically nonlinear finite element analysis with beams |
| 3 |
Jan. 16, 2024:
Mobility analysis; how to identify the degrees of freedom and the number of required actuators Reinforcing the concept of virtual rigid segments in the extended Gurbler's formula Jan. 18, 2024: Maxwell's rule and Calladine's extension How to compute and interpret DoF of compliant mechanisms using the extended Grubler's formula |
Mobility analysis of compliant mechanisms Delineating DoFs (degrees of freedom) and SoSSs (states of self-stress) Grubler's formula extended for compliant mechanisms |
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| 4 |
Jan. 23, 2024:
Degrees of freedom and states of self-stress (contd.)
Jan. 25, 2024: How to delineate DoF and SoSS using compatibility and force-equilibrium matrices of a truss. Matlab program for the mobility analysis of 2D and 3D trusses; nullspace interpretation of DoF and SoSS modes. | - | Matalb code and data files for planar truss mobility analysis |
| 5 |
Jan. 30, 2024:
Classification of compliant mechanisms Characterizing the stiffness of elastic pairs Compliant hingers and sliders; folded-beam suspension mechanism Myosotis method for beam deformation analysis Feb. 1, 2024: Myosotis method (contd.) with examples Multi-axis stiffness of the folded-beam suspension | Elastic pairs | 3D beam fea code (linear) |
| 6 |
Feb. 6, 2024:
Micromechanical suspensions A case study of a micromachined accelerometer Feb. 8, 2024: Instant centre method of design of compliant mechanisms Examplification of the instant centre method in multiple stages |
Instant center method Micromachined accelerometers |
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| 7 |
Feb. 13, 2024:
Mechanical advantage aspects of compliant mechanisms Three types of mechanical advantages and their implication Feb. 15, 2024: Spring-lever (SL) model of compliant mechanisms for abstraction of static behaviour kci, kco, and n The equivalence with two DoF (single-input-single-output) model of CMs |
Mechanical advanatges aspects of CMS by Salomon and Midha Spring-lever modeling of CMs |
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| 8 |
Feb. 20, 2024:
Elastica analysis
Feb. 22, 2024: Elastica analysis and PRB Burns and Crossley's kinematic approximation of a cantilever with a rigid bar of shortened length Howell and Midha's kinetostatic approximation of a cantilever with a rotation spring of constant stiffness |
Elastica analysis Elastica similarity analysis 1 Elastica similarity analysis 2 Pseudo-rigid-body (PRB) kinematic model Pseudo-rigid-body (PRB) kinetoelastic model |
In-class 30-min quiz on Feb. 20. |
| 9 |
Feb. 27, 2024:
Principle of virtual work and force-equilibrium equation Kinetoelastic equations and precision point synthesis for torque-angle specifications Feb. 29, 2024: Discussion of homework problems | Force-equilibrium equation using PRB | - |
| 10 |
Mar. 5, 2024:
Synthesis equations for constant-force compliant mechanism
Mar. 7, 2024: Mid-term examination | - | - |
| 11 |
Mar. 12, 2024:
Precision point synthesis: variable, equations, free choices
Mar. 14, 2024: Kinetoelastic synthesis using PRB and precision points synthesis | - | - |
| 12 |
Mar. 19, 2024:
Spring-mass-lever model; energetic approach to arrive at m_ci and m_co
Mar. 21, 2024: Selection-based design of compliant mechanisms using spring-lever and spring-mass-lever models Static balancing with zero-free-length springs |
Spring-mass-lever models |
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| 13 |
Mar. 26, 2024:
Static balancing: force-force; force-spring; and spring-spring Concept of constant potential energy and zero-free-length springs Mar. 28, 2024: Bistability, snap-through; analysis of shallow arches; energy method |
An ME project on static balancing Static balancing using auxiliary springs Static balancing techniques applied to compliant mechanisms Static balancing of cognates of the four-bar linakge with a spring load |
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| 14 |
Apr. 2, 2024:
Topology optimization of compliant mechanisms Topology optimization using YinSyn Apr. 4, 2024: Quiz 2 (8:30 AM to 9:30 AM); open everyting |
Topology optimization of compliant mechanisms using beam elements and mutual strain energy and strain energy formulation Topology optimization of compliant mechanisms with distributed compliance YinSyn: topology optimization code for compliant mechanisms and stiff structures |
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| 15 |
Apr. 9, 2024:
Non-dimensional models of beams undergoing large displacements Non-dimensional modeling of compliant mechanisms Building block method of designing compliant mechanisms; compliance ellipsoid Apr. 11, 2024: Comparison of design methods for compliant mechanisms |
Non-dimensionalization of compliant mechanisms response Building block method of compliant mechanisms Comparison of several design methods of compliant mechanisms |
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| 16 | Apr. 16, 2024: Advanced applications of compliant mechanisms | - | - |