Welcome to “The FACTs of Mechanical Design!” I'm Professor Jonathan Hopkins and my area of study involves the design, optimization, and fabrication of flexible mechanisms, structures, and materials (e.g., compliant mechanisms, architected metamaterials, soft robots, origami, and MEMs devices) that deform to achieve extraordinary capabilities. In this channel, I will be posting university lectures, professionally edited courses, and other videos that highlight specific mechanisms that I have designed.
If you'd like to better understand my research, you can check out my group's website: www.flexible.seas.ucla.edu If you'd like to download part files of the mechanisms that I feature on the channel, you can download them here: www.thingiverse.com/thefactsofmechanicaldesign/designs If you'd like to donate to my channel to help offset the personal cost to produce this content, you can do so using PayPal: PayPal.me/FACTsMechDesign Your support is much appreciated!
… What a waste of your time and people’s time. Show what it has learnt. This is too much engineering with no practical use. It is basically just slave research for other people’s research to build on or use. Lacks vision and goal.
Im a piano builder since 10 years and I own a 3D printer since a year, and I printed mechanisms and compliant mechanism to learn more how I can bring 3D prints in the piano action. I want now to remove all strings and joints to compliant mechanism. Thank you for your teachings, I will dismantle the process in small simple parts and test everything
### The FACT Design Process [Lecture 5 Part 7] 1. (6:26): Specify desired DOFs. 2. (8:35): Consult the FACT library and identify the corresponding freedom and constraint spaces. 3. (11:42): Determine the number of non-redundant constraints needed. 4. (12:30): Select or deduce the appropriate sub-constraint space. 5. (13:21): Pick constraints within the sub-constraint space, considering fabrication, symmetry, and parasitic errors. 6. (16:08): Over-constrain if needed, prioritizing minimal redundancy and assembly considerations. ### Example Applications [Lecture 5 Part 7] * Spherical Joint (6:26): Three intersecting rotations are achieved by a sphere in the freedom space and three independent constraints. * Micro Mirror Array (18:11): Tip and tilt motion is achieved by a disk in the freedom space. Exploration of various sub-constraint spaces leads to a design with a blade and a wire, potentially over-constrained for symmetry and ease of fabrication. * Advanced Applications (14:18 [time is wrong]): Micromirror arrays with piston motion for phase modulation and light steering, enabling autostereoscopic displays, force fields, improved 3D printing, and more. ### Key Takeaways [Lecture 5 Part 7] * (17:59): FACT provides a comprehensive and systematic approach to designing compliant mechanisms for parallel systems. * (17:59): It leverages visual geometric shapes and intuitive instructions to guide the design process. * (17:59): The FACT library and sub-constraint spaces streamline design by offering a finite set of possibilities and ensuring non-redundancy. * (17:59): Understanding FACT empowers designers to efficiently explore the design space, infuse their common sense, and generate innovative solutions.
## Lecture 4: Compliant Mechanism Design Theories and Constraint-Based Design Principles This lecture covers three design theories for compliant mechanisms and delves into the principles of constraint-based design. ### Compliant Mechanism Design Theories * *Topology Optimization:* * *Concept:* A computational approach where a computer iteratively removes or adds material (represented as nodes and beams or a mass distribution) within a defined design space to optimize a mechanism's performance based on specified functional requirements. * *Strengths:* * Generates optimal, often non-intuitive designs that humans might not conceive. * Suitable for complex designs. * *Limitations:* * Resulting designs can be impractical to fabricate (e.g., complex geometries, thin features). * Difficulty in incorporating common sense constraints (e.g., feature size, material limitations). * Computationally expensive, especially for 3D and complex motions. * Limited user input during the design process. * *Pseudo-rigid Body Model (PRBM):* * *Concept:* A mathematical approach that models flexible members as rigid links connected by pin joints and torsional springs, approximating the compliant mechanism's behavior. * *Strengths:* * Leverages established rigid mechanism theory for design and analysis. * Simplifies analysis of large deformation compliant mechanisms. * *Limitations:* * Requires familiarity with the model and its application. * Primarily a tool for analysis, design requires more skill. * Limited to existing models, less suitable for precision applications. * More challenging to apply in 3D. * *Constraint-Based Design:* * *Concept:* An intuitive approach based on understanding how constraints (flexible elements) control degrees of freedom (directions of high compliance). * *Characteristics:* * Less systematic and rigorous, relies on experience and creativity. * Designs often resemble rigid bodies with strategically placed flexible elements. ### Principles of Constraint-Based Design * *Degrees of Freedom:* * Defined as directions of high compliance, where constraints do not restrict motion. * In 2D, an unconstrained body possesses three degrees of freedom (two translations and one rotation). * In 3D, an unconstrained body possesses six degrees of freedom (three translations and three rotations). * Visualized as infinitesimal motions, not finite deformations. * *Maxwell's Equation:* * Relates the number of non-redundant constraints (C) to the number of degrees of freedom (R). * In 2D: 3 - C = R * In 3D: 6 - C = R * *Exact Constraint:* * Each constraint does a unique job of restricting a single degree of freedom. * Critical for precision applications as it ensures repeatability and accuracy. * Totally exactly constrained systems have zero degrees of freedom and become structures. * *Over Constraint:* * Opposite of exact constraint. * Occurs when more constraints than necessary are applied, leading to redundancy. * Can cause stress build-up, making the system prone to errors and failure. * Blades and wire flexures can contribute to over-constraint. * *Rule of Complementary Patterns:* * *Concept:* Defines the relationship between constraint lines (blue) and rotation lines (red) to determine degrees of freedom. * *Rule:* Every rotation line must intersect every constraint line at least once (including at infinity for parallel lines). * *Application:* * Draw blue constraint lines through the axis of wire flexures or represent the planes of blade flexures. * Identify red rotation lines that intersect all blue lines, including at infinity. * Red lines in finite space represent rotations, while red lines at infinity represent translations. ### Key Principles: * *One constraint kills at most one degree of freedom.* * *Degrees of freedom are not fixed to a specific coordinate system and can move within the system.* * *Blades themselves are not inherently over-constrained, but multiple blades can lead to over-constraint.* * *Parallel systems (two rigid bodies directly connected by flexible elements) cannot be under-constrained.*
*Part 6: General Systems (**21:52**):* * *Series Systems (**5:34**):* Elements experience the same force but different displacements. Equivalent compliance is the sum of individual compliances. * *Hybrid Systems:* Combinations of parallel and series. * *Interconnected Hybrid Systems:* Intermediate bodies connected, preventing simplification into series/parallel. * *General Stiffness Matrix (**17:48**):* Requires a more complex approach (beyond the scope of the lecture), but a paper and MATLAB script were provided for reference. * *General Mass Matrix (**24:46**):* Similar to parallel systems, but with a larger matrix to include all moving bodies. * *Infinite Mode Shapes and Frequencies (**28:08**):* In reality, systems have distributed mass and compliance, leading to an infinite number of mode shapes and frequencies. The lecture concluded by emphasizing the significance of understanding stiffness and mass matrices for analyzing and designing compliant mechanisms.
*Part 5: Mode Shapes and Natural Frequencies (**22:47**):* * *Natural Frequency:* Frequency at which a system vibrates without external force. * *1D Proof (**23:00**):* For a point mass on a spring, `ωn = sqrt(k/m)` * *3D Eigenvalue Problem (**27:04**):* * Set equations of motion to zero (`Wrench = 0`) * Eigenvalues of `Mtw^(-1) * Ktw` represent squared natural frequencies * Eigenvectors represent mode shapes (twist vectors) * *Example Calculation (**9:07**):* Found 6 mode shapes and corresponding natural frequencies for the parallel system example.
*Part 4: Mass Matrix (**4:04**):* * *Assumptions:* * Stages are infinitely rigid (no compliance) * Flexible elements have no mass (all stiffness) * *Steps to Calculate Mass Matrix (**5:49**):* * Find mass of the stage (`m = ρV`) * Find center of mass (by inspection or integration) * Define new coordinate system at the center of mass, aligned with principal axes * Define unit vectors `n1`, `n2`, `n3` along principal axes * Construct transformation matrix `N` using center of mass position vector and `n1`, `n2`, `n3` * Calculate mass moments of inertia (`Ix`, `Iy`, `Iz`) about principal axes * Construct inertia matrix `In` (diagonal with mass moments and mass) * Obtain the mass matrix using: `Mtw = N * In * N^(-1)` * *Considering Flexure Mass (**15:09**):* * Approximate by adding half the flexure length as rigid mass to the stage
*Part 3: Example Calculation (**23:54**):* * Worked through a detailed example to find the stiffness matrix of a parallel system with four wire flexures.
*Part 2: Parallel System Stiffness* * *Parallel Systems (**2:57**):* * Two rigid bodies connected directly by flexible elements * *Displacement Twists (**4:02**):* * 6-element vector representing infinitesimal rotations and translations of a point on the stage * Defined with respect to a global coordinate system * *Constructing the Stiffness Matrix (**6:45**):* * Define local coordinate system for each element at its attachment point * Define vectors: `L` (position vector) and `n1`, `n2`, `n3` (unit vectors along local axes) * Construct transformation matrix `N` using `L`, `n1`, `n2`, `n3` * Calculate element stiffness matrix `S` using material properties and geometry * Apply transformation to obtain global stiffness matrix for each element * *Total Stiffness Matrix (**22:00**):* * Sum the stiffness matrices of all elements in parallel
## Lecture 2 Part 4 Summary *9:12** Analogies Between Velocity Twists and Wrench Lines (Forces and Moments):* * The lecture emphasizes the analogy between velocity twists and wrench lines, which represent forces and moments. * Wrench lines are depicted as orange lines, analogous to green screw lines. * They are described by 6x1 vectors, where the top three components represent force (F) and the bottom three represent torque or moment (τ). * Similar to screw lines, they have a location vector (r) pointing to any point on the line of action and a "q" value, analogous to pitch, representing the coupled moment per force ratio. *13:48** Force, Moment, and Wrench Types:* * A wrench with q=0 represents a pure force, depicted as a blue line. * The torque is calculated by the cross product of the location vector and force: τ = r x F. * A wrench with q=∞ represents a pure moment, analogous to a translation. * Pure moments have no specific location. * A wrench with finite q combines force and torque, similar to a screw motion. *17:00** Key Difference in Organization:* * One crucial difference between velocity twists and wrench lines is the order of angular and linear components. * In velocity twists, angular velocity (ω) is on top, and linear velocity (v) is on the bottom. * In wrench lines, force (F), a linear quantity, is on top, and torque (τ), an angular quantity, is on the bottom. * This difference in organization will be significant in later concepts. *17:52** Final Takeaways:* * The lecture stresses the importance of understanding the analogies between velocity twists and wrench lines, as they share many mathematical concepts and relationships. * Although mathematically challenging, mastering these concepts is crucial for grasping the later principles of compliant mechanism design. * Encourage rewatching the lecture multiple times and practicing the examples to solidify understanding. * Emphasize that even without fully understanding the derivations, students can still apply the concepts and succeed in the course.
## Lecture 2 Part 3 Summary *8:58** Transforming Twist Vectors between Coordinate Systems:* * The lecture then delves into a crucial concept: transforming twist vectors from one coordinate system to another. * This is important for analyzing motion relative to different frames of reference. * A new coordinate system (x', y', z') is introduced, and the goal is to find the twist vector (t') in this new frame, given the original twist vector (t) in the global frame (x, y, z). *11:43** Constructing the Transformation Matrix (N):* * The transformation involves constructing a 6x6 matrix called "N." * N incorporates information about the relative positions and orientations of the two coordinate systems. * This includes: * A location vector (l) pointing from the origin of the global frame to the origin of the new frame. * Three unit vectors (n1, n2, n3) aligned with the axes of the new coordinate system but defined with respect to the global frame. *17:30** Linear Combination of Degrees of Freedom:* * The key insight behind the transformation is that a free body has six degrees of freedom: three rotations and three translations. * By linearly combining these six degrees of freedom with appropriate magnitudes, any desired motion can be achieved. *24:21** Using N for Transformation:* * The equation t' * N = t establishes the relationship between the twist vectors in both frames. * Solving for t' involves inverting the matrix N: t' = t * N⁻¹. *26:50** Transformation Example:* * A detailed example walks through the process of constructing the N matrix and using it to transform a twist vector from the global frame to a new frame. * The results obtained through this matrix transformation method match the results obtained by directly defining the screw parameters in the new frame, validating the approach. *5:39** Displacement Twists, Velocity Twists, and Acceleration Twists:* * The lecture concludes by introducing variations of twist vectors: * *Displacement twists:* obtained by multiplying velocity twists with an infinitesimal time increment (Δt). They represent infinitesimal displacements in rotation and translation. * *Acceleration twists:* derived by taking the time derivative of velocity twists. They represent angular and linear accelerations.
## Lecture 2 Part 2 Summary ****2:54** Visualizing c x ω:** * Imagine the global coordinate system aligned with the rotational axis. * Vector c points from the origin to any point on the axis. * As the body rotates, the origin will move in a circle perpendicular to both c and ω. * The direction of this movement is the direction of v, which aligns with the right-hand rule applied to c x ω. ****9:03** Visualize Screw Lines:** * Represented as green lines with a squiggly arrow, indicating a combination of rotation and translation along the line. * Like rotational twist vectors, they have a location vector (c) and angular velocity vector (ω). * Introduce a "pitch" (p), a scalar representing the coupled translation per rotation. ****11:34** Pitch:** * Represents the amount of translation along the screw line for a given rotation angle. * Analogy: Think of a screw threading into a wall; its translation is coupled to its rotation. * Units are meters per radian (translation per rotation). ****12:59** Screw Twist Vectors:** * Defined similarly to rotational twist vectors but with an additional term for the pitch: v = c x ω + pω. * The linear velocity of the origin is the sum of two vectors: one due to rotation (c x ω) and one due to translation along the screw line (pω). ****17:57** General Twist Vectors & Chasles' Theorem:** * Chasles' theorem states that all instantaneous motions can be described as screws. * Rotations are screws with zero pitch (p=0). * Translations are screws with infinite pitch (p=∞). * Any finite pitch results in a screw motion combining rotation and translation. *28:20** Decomposing Twist Vectors:* * Given a twist vector (t), you can decompose it to find the angular velocity (ω), linear velocity (v), pitch (p), and location vector (c). * Pitch (p) can be found by: p = (ω • v) / (ω • ω), where "•" denotes the dot product. * Location vector (c) can be found using the cross product formula and the equation v = c x ω + pω. This involves solving a system of equations, some of which may allow for multiple solutions. *21:11** Translations as Screws with Infinite Pitch:* * When p=∞, the twist vector represents a pure translation. * This leads to ω = 0, and c becomes irrelevant as any location along the translational direction is equivalent. * The linear velocity (v) is determined by the product of zero (ω) and infinity (p), which can be any finite real number based on the specific translation. *24:48** Key Takeaways about Translations:* * Translations have no inherent location because any point along the translational direction is equivalent. * A single linear velocity vector is sufficient to define a pure translation for a rigid body. *25:59** Decomposing Twist Vectors: Example:* * A numerical example is presented where a given twist vector is decomposed to find its pitch and location vector. * The example highlights that the location vector (c) can have multiple solutions, as long as it points to a point on the screw line.
## Lecture 2 Part 1 Summary ****0:01** Introduction:** * Lectures 2 and 3 are math-heavy and crucial for understanding the compliant mechanism design approach. * Don't be discouraged by the math; the rest of the course is more visual and fun. * Rewatch lectures 2 and 3 multiple times to fully grasp the concepts. * This lecture focuses on screw theory kinematics, specifically translational and rotational velocity vectors. ****1:51** Translational/Linear Velocity Vectors:** * Represented as 3x1 vectors, describing a body's velocity in 3D space (x, y, z). * Possess magnitude (speed) and direction but no inherent location. * Example: A block translating along the y-axis with velocity "vy" can have the velocity vector drawn anywhere as long as direction and magnitude are maintained. * In rotations, every point on a body has a different linear velocity vector associated with its location, but the 3x1 vector itself doesn't capture location information. ****8:36** Angular/Rotational Velocity Vectors:** * Also 3x1 vectors, describing a body's rotation speed and direction. * Like translational vectors, they have magnitude and direction but no inherent location. * The vector's direction aligns with the axis of rotation, but it doesn't specify the axis's location. * Example: A block rotating 30 degrees in a second can achieve this with different axes and paths, all resulting in the same average angular velocity vector. * Every point on a body rotating around an axis shares the same angular velocity vector. ****18:58** Confusing Takeaways:** * Knowing the angular velocity vector of one point reveals the angular velocity of all points on a rotating body. However, it doesn't reveal the axis's location. * Knowing the linear velocity vector of one point reveals the velocity of all points only if the body is purely translating. Otherwise, it only describes that single point's motion. * To fully describe a body's motion, you need both the angular velocity vector and the linear velocity vector of a single point. ****27:58** Twist Vectors:** * 6x1 vectors combining angular velocity (ω) and linear velocity (v) of the global coordinate system origin. * The top three components are ω, and the bottom three are v, both defined with respect to the global coordinate system (x, y, z). * Used in screw theory to package the motion of a body by capturing the motion of a single point attached to the body. ****29:35** Rotational Twist Vectors:** * Have a red "line of action" representing the axis of rotation. * The linear velocity (v) of the origin is calculated as the cross product of a location vector (c) and the angular velocity vector (ω): v = c x ω. * Vector c can point to any point on the axis of rotation. This is because the perpendicular distance between the origin and the axis remains constant.
*Summary of Flexure Design Principles:* * *Increase the first natural frequency to improve system performance:* (0:59) * Stiffen flexures (increase k). * Reduce mass (decrease m). * *Avoid aligning mode shape directions with sensitive directions:* (1:47) * Sensitive vibration directions should be perpendicular to the desired motion. * *Damping Vibrations:* (2:56) * *Passive Damping:* Immerse in viscous fluid (honey, water), attach rubber strips (watch out for hysteresis). (3:04) * *Active Damping:* Expensive but effective, uses actuators and sensors with closed loop control. (3:59) * *Input Shaping:* Open loop control, characterize system and apply a specifically shaped force to achieve desired displacement without vibrations. (5:18) * *Material Selection:* (7:18) * *Avoid:* Polymers (creep, hysteresis), high temperatures (creep, stress relaxation). (7:34) * *Ideal:* Metals (aluminum, titanium, stainless steel, invar), sometimes ceramics (brittle). (8:17) * *Key Material Properties:* (8:42) * *Range:* Choose materials with a high yield strength to modulus ratio. (8:46) * *Thermal:* Choose materials with a high thermal diffusivity to thermal expansion coefficient ratio. (11:07) * *Dynamics:* Choose materials with a high Young's modulus to density ratio. (12:55) * *Fabrication:* Not covered due to battery limitations. (15:08) *Deutsche Zusammenfassung der Prinzipien des Flexure-Designs:* * *Erhöhen Sie die erste Eigenfrequenz, um die Systemleistung zu verbessern:* (0:59) * Versteifen Sie die Flexuren (erhöhen Sie k). * Reduzieren Sie die Masse (verringern Sie m). * *Vermeiden Sie es, die Richtungen der Eigenformen mit empfindlichen Richtungen auszurichten:* (1:47) * Empfindliche Schwingungsrichtungen sollten senkrecht zur gewünschten Bewegung stehen. * *Dämpfung von Schwingungen:* (2:56) * *Passive Dämpfung:* Eintauchen in viskose Flüssigkeit (Honig, Wasser), Anbringen von Gummistreifen (achten Sie auf Hysterese). (3:04) * *Aktive Dämpfung:* Teuer, aber effektiv, verwendet Aktuatoren und Sensoren mit Regelung. (3:59) * *Eingangsformung:* Regelung mit offenem Regelkreis, charakterisieren Sie das System und wenden Sie eine speziell geformte Kraft an, um die gewünschte Verschiebung ohne Schwingungen zu erreichen. (5:18) * *Materialauswahl:* (7:18) * *Vermeiden Sie:* Polymere (Kriechen, Hysterese), hohe Temperaturen (Kriechen, Spannungsrelaxation). (7:34) * *Ideal:* Metalle (Aluminium, Titan, Edelstahl, Invar), manchmal Keramik (spröde). (8:17) * *Wichtige Materialeigenschaften:* (8:42) * *Bereich:* Wählen Sie Materialien mit einem hohen Verhältnis von Streckgrenze zu Elastizitätsmodul. (8:46) * *Thermisch:* Wählen Sie Materialien mit einem hohen Verhältnis von Temperaturleitfähigkeit zu Wärmeausdehnungskoeffizient. (11:07) * *Dynamik:* Wählen Sie Materialien mit einem hohen Verhältnis von Elastizitätsmodul zu Dichte. (12:55) * *Fertigung:* Nicht behandelt aufgrund von Batteriebeschränkungen. (15:08) i used gemini 1.5 flash and pro
*Hysteresis Loop and Flexure Design: Summary* This transcript provides a detailed explanation of hysteresis loops and their impact on flexure design, highlighting best practices for achieving high precision and repeatability in mechanical systems. *Key Points:* * *Hysteresis Loop (**0:00**):* * Caused by friction at sliding joints, resulting in different force-displacement curves for loading and unloading. * Represents energy loss due to friction, impacting repeatability. * Requires knowledge of loading history to understand force-displacement relationship. * *Minimizing Hysteresis (**1:28**):* * *Material Choice (**7:00**):* Single-piece, single-crystal materials minimize internal friction and micro-slip, improving repeatability. * *Joint Design (**8:02**):* Avoid sliding joints; utilize glue, clamp blocks, and strategic bolt placement to distribute strain and minimize micro-slip. * *Stress Management (**3:41**):* Keep stress levels below 20% of the yield strength to prevent permanent deformation and micro-slip. * *Actuator Choice (**6:20**):* Employ non-contact actuators (e.g., voice coils) to eliminate friction and enhance precision. * *Flexure Design Considerations:* * *Thermal Expansion (**19:11**):* Design for thermal stability to mitigate unwanted movement caused by temperature variations. Symmetrical designs can help reduce thermal instability. * *Vibrations (**23:05**):* * Understand the concepts of natural frequencies and mode shapes. * Design flexures and supporting structures to avoid resonance and minimize unwanted vibrations. * *Accuracy and Calibration (**12:19**):* * Manufacturing tolerances inevitably lead to deviations between designed and actual stiffness of flexures. * Calibration is essential to achieve accuracy after accounting for these variations. * *Illustrative Example (**17:28**):* A 5% tolerance in the dimensions of a flexure can result in a significant (71%) change in stiffness, highlighting the importance of calibration. * *Key Takeaways:* * Precision and repeatability are paramount for achieving high accuracy in mechanical systems. * Meticulous design choices are crucial to minimize hysteresis and other factors affecting precision. * Calibration is a fundamental step to ensure accuracy in the presence of inevitable variations caused by manufacturing and environmental factors. *Deutsch: Hysterese-Schleife und Biegebalken-Design: Zusammenfassung* Dieses Transkript bietet eine detaillierte Erklärung von Hysterese-Schleifen und deren Auswirkungen auf das Design von Biegebalken. Es hebt die besten Praktiken hervor, um hohe Präzision und Wiederholbarkeit in mechanischen Systemen zu erreichen. *Schlüsselpunkte:* * *Hysterese-Schleife (**0:00**):* * Entsteht durch Reibung an gleitenden Gelenken, was zu unterschiedlichen Kraft-Verformungs-Kurven beim Beladen und Entladen führt. * Stellt den Energieverlust durch Reibung dar und beeinflusst die Wiederholbarkeit. * Erfordert die Kenntnis der Belastungshistorie, um die Kraft-Verformungs-Beziehung zu verstehen. * *Minimierung von Hysterese (**1:28**):* * *Materialwahl (**7:00**):* Einteilige, einkristalline Materialien minimieren die innere Reibung und Mikrorisse, was die Wiederholbarkeit verbessert. * *Gelenkdesign (**8:02**):* Vermeidung von gleitenden Gelenken; Verwendung von Klebstoff, Klemmblöcken und strategischer Platzierung von Schrauben, um die Spannung zu verteilen und Mikrorisse zu minimieren. * *Spannungsmanagement (**3:41**):* Halten Sie die Spannungswerte unter 20 % der Streckgrenze, um dauerhafte Verformungen und Mikrorisse zu vermeiden. * *Aktuatorwahl (**6:20**):* Verwenden Sie kontaktlose Aktuatoren (z. B. Sprachspulen), um Reibung zu vermeiden und die Präzision zu verbessern. * *Designüberlegungen für Biegebalken:* * *Wärmeausdehnung (**19:11**):* Designen Sie für thermische Stabilität, um unerwünschte Bewegungen durch Temperaturschwankungen zu minimieren. Symmetrische Designs können dazu beitragen, thermische Instabilität zu reduzieren. * *Schwingungen (**23:05**):* * Verstehen Sie die Konzepte von Eigenfrequenzen und Schwingungsformen. * Konstruieren Sie Biegebalken und unterstützende Strukturen, um Resonanz zu vermeiden und unerwünschte Schwingungen zu minimieren. * *Genauigkeit und Kalibrierung (**12:19**):* * Fertigungstoleranzen führen unweigerlich zu Abweichungen zwischen der geplanten und der tatsächlichen Steifigkeit von Biegebalken. * Kalibrierung ist unerlässlich, um nach der Berücksichtigung dieser Abweichungen die Genauigkeit zu erreichen. * *Beispiel (**17:28**):* Eine Toleranz von 5 % bei den Abmessungen eines Biegebalkens kann zu einer signifikanten (71 %) Veränderung der Steifigkeit führen, was die Bedeutung der Kalibrierung unterstreicht. * *Schlüsselerkenntnisse:* * Präzision und Wiederholbarkeit sind von entscheidender Bedeutung, um eine hohe Genauigkeit in mechanischen Systemen zu erreichen. * Sorgfältige Designentscheidungen sind entscheidend, um Hysterese und andere Faktoren, die die Präzision beeinflussen, zu minimieren. * Kalibrierung ist ein grundlegender Schritt, um trotz unvermeidbarer Abweichungen durch Fertigung und Umweltfaktoren die Genauigkeit sicherzustellen. i used gemini 1.5 flash and pro
*Challenges of Compliant Mechanisms:* (0:19) * More difficult to design and analyze. * May store unwanted energy. (1:04) * Fatigue can be an issue. (2:12) * Limited range of motion. (4:15) *Overcoming Challenges:* * Design and analysis approaches exist to make design more approachable. (0:40) * Multi-stable mechanisms and plastic deformation can mitigate energy storage. (1:17) * Material selection and design can minimize fatigue. (2:28) * Strategies like stacking and nesting can increase range of motion. (5:17) *Flexures:* (7:11) * Subset of compliant mechanisms. * Consists of rigid bodies connected by compliant elements. * Guide motion in a well-defined manner. *Types of Flexure Systems:* (9:15) * Parallel: Two rigid bodies directly connected by flexure elements. * Serial: Multiple parallel systems stacked or nested in series. * Hybrid: Combination of parallel and serial systems. *Flexure Applications:* (15:49) * Microscopy stages * Optical mounts (telescopes, CD players) (16:48) * Micro-electro-mechanical systems (MEMS) (17:31) *Advantages of Flexures:* (15:49) * High precision and repeatability (sub-nanometer resolution). (19:50) * Ideal for small-scale applications. (17:31) * Relatively inexpensive compared to air or magnetic bearings. (20:47) * Can be calibrated to achieve high accuracy. (26:11) *Precision, Accuracy, and Repeatability:* (23:30) * Accuracy: Difference between the intended and average actual position. * Precision: Measure of spread or repeatability of motion. * Flexures offer high precision and repeatability, but may require calibration for accuracy. (26:11) *Why Flexures are Precise:* (29:13) * Relative motion is achieved by stretching/compressing atomic bonds. * As long as bonds are not broken, deformation is highly repeatable. * This leads to superior precision compared to systems with friction. i used gemini 1.5 pro (2024-05-15)
*Introduction:* * *[**0:00**]* Axiomatic design favors uncoupled design parameters and function requirements for simplicity and ease of fixing issues. * *[**3:19**]* Nature, on the other hand, exhibits highly coupled and complex designs. * *[**4:22**]* Rigid mechanisms are preferred over compliant ones due to their predictability and ease of design. * *[**6:05**]* Advancements in design tools are making compliant mechanism design easier, leading to superior performance. *Compliant Mechanism Applications:* * *[**6:38**]* *Chainsaw Clutch:* Replacing multiple rigid parts and a spring with a single compliant piece, improving weight and ease of manufacturing. * *[**9:04**]* *Zero Stiffness Joint:* Achieves high stiffness in all directions except for rotation, providing near-zero resistance in a specific rotational direction. * *[**12:46**]* *Lattices:* Architected materials using zero stiffness joints, enabling complex kinematics with a single piece. * *[**13:30**]* *Flexure Coupling:* Accommodates misalignment between rotating shafts without the drawbacks of rigid couplings (clatter, friction, wear). * *[**14:56**]* *Overrunning Clutch:* Allows rotation in one direction only, engaging a ratchet mechanism when rotating in the opposite direction. * *[**15:55**]* *Multistability:* Designs with multiple stable states, achieved by strategically utilizing compliance and strain energy. * *[**17:40**]* *Lamina Emergent Mechanism:* 3D mechanisms created by deforming a single planar sheet, simplifying fabrication and assembly. * *[**20:04**]* *Origami and Kirigami:* Art forms utilizing compliance and selective cuts to create compact deployable structures. *Advantages of Compliant Mechanisms:* * *[**22:26**]* *Reduced Part Count:* Often requiring fewer parts compared to traditional mechanisms. * *[**22:26**]* *Easier Fabrication and Assembly:* Simplifying manufacturing and assembly processes, often resulting in monolithic designs. * *[**23:45**]* *Lighter Weight:* Utilizing less dense materials and eliminating bulky components. * *[**24:08**]* *Reduced Cost:* Lower material usage, simpler fabrication, and assembly contribute to significant cost reduction. * *[**24:20**]* *Reduced Friction and Wear:* Eliminating sliding and pin joints, resulting in less friction, heat generation, and wear. * *[**25:04**]* *Reduced Maintenance:* Fewer parts and lack of wear contribute to lower maintenance requirements. * *[**25:56**]* *Energy Storage:* Natural ability to store strain energy, eliminating the need for additional springs. * *[**26:14**]* *Scalability:* Easily miniaturized or scaled up without significant changes in design principles. * *[**27:34**]* *Precision:* Achieving high precision due to the inherent deterministic nature of deformation. *Conclusion:* * *[**28:23**]* Compliant mechanisms offer numerous advantages over traditional rigid mechanisms, particularly in areas like cost, weight, and precision. * *[**28:23**]* Understanding compliant mechanisms can unlock new design possibilities and lead to innovative solutions. i used gemini 1.5 pro (2024-05-15)
*What are Compliant Mechanisms?* [1:16] * *Mechanisms:* Devices that transfer or transform motion, force, or energy. * *Compliant Mechanisms:* Mechanisms with flexible elements that bend and deform to achieve motion, storing strain energy in the process. *Examples of Compliant Mechanisms:* [3:03] * *Ancient:* Bow and arrows, crossbows, catapults, bellows. * *Modern:* CD cases, backpack straps, shampoo caps, tweezers, electric shavers, leaf springs, skateboards, diving boards, prosthetics, tennis rackets, bowflex machines, playgrounds. * *Medical:* Endoscopic tools, clamps, prosthetic knee. [8:25] * *Material Properties:* Architectured materials with engineered properties (e.g., negative Poisson ratio). [11:34] * *Energy Harvesting:* Devices that capture ambient vibrations and convert them into electricity. [13:46] *Why Nature Prefers Compliance:* [16:49] * *Efficiency:* Compliant structures require less energy for movement and maneuvering. * *Robustness:* Flexibility allows for impact absorption and stress distribution, preventing damage. [18:54] * *Adaptability:* Compliance enables accommodation of imperfections and changing environments. [20:47] * *Versatility:* Allows for complex motions and functionalities with fewer components. [22:18] *Challenges of Compliant Mechanism Design:* [26:28] * *Complexity:* Designing compliant mechanisms is more intricate than rigid-body systems. * *Uncoupled Design:* Achieving independent control over functional requirements is difficult due to the interconnected nature of compliant elements. [27:04] *Future of Compliant Mechanisms:* [23:52] * *Robotics:* Nature-inspired robots incorporating compliance for enhanced adaptability and efficiency. * *Aerospace:* Compliant wings for improved maneuverability and fuel efficiency. * *Continued Exploration:* Expanding applications in various fields due to their inherent advantages. i used gemini 1.5 pro (2024-05-15)
Wow. This concept is hugely misrepresented here. It is not about designing "new materials", it is about designing robotic muscles (maybe). This work looks real/legitimate, however the puny and overly complicated electromagnet at the heart of each truss beam member is many orders of magnitude weaker than all metals and probably most plastics (the modulus of elasticity for steel is 30 million pounds per square inch [psi] and 300,000 psi for most plastics). Therefore claiming, as this video does, that this tech is good for aircraft wings, building beams or body armor is a massive stretch. I see almost no chance that this manifestation of this concept will ever becoming more than a college lab demo. It is interesting as a mathematical exercise, but the "Devil is in the details". The electronic truss strut muscle they have created, which is basically a solenoid and which has been around forever, is only suitable for light duty. Also, wiring this concept for anything but the small demo unit they showed must be a nightmare and the complexity of it all means the probability of failure, over time, will be large. When redesigning the new electro-strut, please consider a design which provides a solid metal-to-metal rigid connection, but that also can extend/retract in length. Look at current linear actuator tech which employs screws (picture a nut on a regular bolt - turn the bolt and if you hold the nut, it moves up or down). design the pitch of the screw such that it is self locking (means the screw won't start rotating on its own when you apply a tensile or compression load). Also, please remember - Just because something is hard doesn't mean it's worth doing.
For others - at 18:00, when he explains why there's only 3 DOF when it appears there is 4...think about it this way: x&y + y&z can't equal x+2y+z (because there's only 1 y).
In optics we often employ the paraxial approximation, treating any trig function tan(theta)=theta for small angles. This works very well until the angle becomes too large and system behavior is no longer paraxial (mirroring the idea of wire flexures increasing in diameter and therefore increasing angles of blue constraint lines). Interestingly, Maxwell's equations for EM waves can be solved using this paraxial approximation and the solutions for this paraxial wave equation are the modes of free space (or the modes of any waveguide or resonator). I came to your lecture series as a curious optical engineer with a love of flexures and am thoroughly enjoying the beauty and accessibility of FACT synthesis. The symmetries between math and geometry to describe mechanical systems vs. optical systems continue to astound me. As well the guiding force of Maxwell in both disciplines! "Maxwell is never wrong" indeed! :)
Regardless…it’s fascinating to watch a clearly intelligent person who seems to have mind like mine…in that he seems to be constantly linking ideas together and has an internal thought process which is constantly thinking about the relationship between all of those thoughts while trying to stay on topic; and while he knows exactly what he’s talking about, I recognise the same thing happening that happens to me…every now and then he takes a moment to pause, I suspect to keep himself on topic but you can also hear him rapidly finishing a thought aloud and quickly trailing off before saying things such as “but anyway” or pausing and saying…”so, yeah…”. There’s many times he might appear to be thinking about what he’s saying but in my opinion he’s barely having to consciously think about that…I believe he’s thinking about whichever one of those tangential thoughts are intruding themselves as he speaks. A classic case of cognitive overload. 16:19 You see, right there…he suddenly thought about spreading things by 60° being “always magic” and he had to verbalise it…then he moves back on topic by saying “so anyway”. Perfect example.
Thanks for doing this. The videos helped me design some low profile, extremely low force custom momentary switches that mimic capacitive switches for an individual with severe motor disabilities.
