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A Screw-Theoretic Framework for Musculoskeletal Modeling and Analysis

A Screw-Theoretic Framework for Musculoskeletal Modeling and Analysis. Michael J. Del Signore. (mjd24@eng.buffalo.edu). December 16th 2005. Advisor: Dr. Venkat Krovi Mechanical and Aerospace Engineering State University of New York at Buffalo. Agenda. Introduction Background

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A Screw-Theoretic Framework for Musculoskeletal Modeling and Analysis

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  1. A Screw-Theoretic Framework for Musculoskeletal Modeling and Analysis Michael J. Del Signore (mjd24@eng.buffalo.edu) December 16th 2005 Advisor: Dr. Venkat Krovi Mechanical and Aerospace Engineering State University of New York at Buffalo

  2. Agenda • Introduction • Background • Case Scenario • System Modeling • GUI Implementation • Simulation Framework • Mechanical Prototype Design • Future Work • Conclusion Michael J. Del Signore December 16th 2005 Slide 2 of 57

  3. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Motivation • Computational advances in the past decade have revolutionized engineering!! • Improved Infrastructure • Advanced Algorithms and Methodologies • Such advancements have been seen far lesser in other professional arenas – e.g. Biological Sciences • Applications developed within this area could bring about similar advances and benefits. Michael J. Del Signore December 16th 2005 Slide 3 of 57

  4. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Research Issues • Significant gap halting the integration of engineering tools into the Biological Sciences fields. • Need for specialized (problem specific) tools. • Users need to be familiar with use and supporting theory. Three Critical Steps • Model creation with adequate fidelity. • Analysis of various actions/ behaviors. • Iterative testing for refining hypotheses. Powerful Tool • Integration and application of certain engineering principles and techniques into one of the candidate biological sciences fields: Musculoskeletal System Analysis Michael J. Del Signore December 16th 2005 Slide 4 of 57

  5. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Challenges Irregularities Redundancies • Unlike traditional engineering systems, musculoskeletal systems inherently possess considerable irregularities and redundancies. • Multiple Muscles: More actuators than degrees of freedom. • Infinite set of actuator (muscle) forces can produce the same end-effector force. • Complex Asymmetric Geometric Shapes (i.e. muscle, bone). • Each specimen is unique. • Dealing with (trying to simulate) living tissue. • Musculoskeletal analysis tools need to take these characteristics into account. Michael J. Del Signore December 16th 2005 Slide 5 of 57

  6. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Existing Tools • Traditional Articulated Mechanical System Analysis Tools • Virtual Prototyping – Virtual product simulation & testing • Examples: VisualNastran, ADAMS, Pro-Mechanica … • Physics, Dynamics, FEA, Contact, Friction – Implementation into real-time control frameworks • The limitations of these tools can be seen when dealing with more complex phenomena and systems. • Complex Geometries • Redundant Actuation • High Number of Contacts Musculoskeletal System Analysis Michael J. Del Signore December 16th 2005 Slide 6 of 57

  7. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Existing Tools • Musculoskeletal System Analysis Tools • In resent years tools have been developed to specifically model and analyze musculoskeletal systems. • Examples: SIMM, AnyBody, LifeMod … • While being successful at handling complex musculoskeletal systems these programs require: • In depth physiological knowledge. • Extensive application specific programming and coding. High Degree of Modeling and Simulation Detail Rapid Real-Time Simulation and Analysis Relatively Impossible Michael J. Del Signore December 16th 2005 Slide 7 of 57

  8. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Research Goal • The development of computational tools that can analyze a redundant musculoskeletal system, incorporating: • An adequate degree of speed • Accurate redundancy resolution • Application in a real-time model based control framework • Undertaken using screw-theoretic modeling methods: • Typically seen with the context of parallel manipulators. • Convenient basis for redundancy resolution and optimization. • Critical aspects addressed within a specific case scenario: • Musculoskeletal Analysis of the Jaw Closure of a Saber-Tooth Cat (Smilodon-Fatalis). Michael J. Del Signore December 16th 2005 Slide 8 of 57

  9. IntroductionBackground Case Scenario Simulation Mechanical Prototype Future Work Conclusion Related Works • Musculoskeletal Modeling • Multi-body Dynamics Approach [Forster, 2003] • Detailed Muscle Modeling (Hill Model) [Wolkotte, 2003] • Muscle Modeling and Software Development (Anybody) [Rasmussen, Damsgaard, Surma, Christensen, de Zee, and Vondrack, 2003] [Konakanchi, 2005] • Screw-Theoretic Modeling • Redundancy Resolution [Firmani and Podhorodeski, 2004] • Parallel Manipulation [Tsi, 1999] • Wrench Based Modeling and Analysis [Ebert-Uphoff and Voglewede, 2004] [Kumar and Waldron, 1988] Michael J. Del Signore December 16th 2005 Slide 9 of 57

  10. l- Pitch, the ratio of translation to rotation. - Moment of the screw axis about the origin. - Unit vector pointing along the direction of the screw axis. - Location of a point on the screw axis. IntroductionBackground Case Scenario Simulation Mechanical Prototype Future Work Conclusion Mathematical Preliminaries Unit Screw • Screw Coordinates The displacement of a rigid body can be defined as a screw displacement, such that its motion can be broken down into a rotation about a unique axis (line) and a translation about the same unique axis called the screw axis. Michael J. Del Signore December 16th 2005 Slide 10 of 57

  11. IntroductionBackground Case Scenario Simulation Mechanical Prototype Future Work Conclusion Mathematical Preliminaries Twists (Velocity) Linear Velocity • Screw Coordinates Angular Velocity Wrenches (Force) Applied Force Moment caused by Fo The displacement of a rigid body can be defined as a screw displacement, such that its motion can be broken down into a rotation about a unique axis (line) and a translation about the same unique axis called the screw axis. Michael J. Del Signore December 16th 2005 Slide 11 of 57

  12. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Musculoskeletal Analysis of the Jaw Closure of the Smilodon • Accurately model and simulate the skull/ mandible musculoskeletal structure of the Smilodon Michael J. Del Signore December 16th 2005 Slide 12 of 57

  13. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Preliminary Simulations • Undertaken using traditional articulated mechanical system tools. • Virtual Simulation of Mechanical Saber-Tooth Cat • Discovery Channel Model Discovery Channel Model Virtual Recreation Michael J. Del Signore December 16th 2005 Slide 13 of 57

  14. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Simulation of Mechanical Smilodon • Implemented using a prescribed motion analysis within VisualNastran • Simulation was successful but more complexity was desired. Michael J. Del Signore December 16th 2005 Slide 14 of 57

  15. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Virtual Prototyping of Smilodon from Fossil Records • VisualNastran simulation created to calculate muscle forces necessary to produce a desired bite force. • Virtual representation created from actual fossil records Michael J. Del Signore December 16th 2005 Slide 15 of 57

  16. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Smilodon Virtual Prototype – VisualNastran • The simulation was met with limitations: • Due to the software's inability to handle redundancy in terms of resolving the multiple muscle forces in an inverse dynamics setting. • These shortcomings provided the motivation for the development of our own low-order computationally tractable model based on screw-theoretic methods. • Constraints were placed on the system to represent: • Muscles  Linear Actuators • Skull/ Mandible Interaction  Revolute Joint • External forces (or alternately a prescribed motion) was applied to the skull as user-specified input to the system. Michael J. Del Signore December 16th 2005 Slide 16 of 57

  17. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Our Model • Representation: • The underlying articulated structure and superimposed musculature is modeled as a redundantly actuated parallel mechanism. • Goal: Development of a Screw-Theoretic Framework • Accurately calculate the muscle forces needed to produce a specific desired applied bite-force. • Serve as a mathematical basis for: • Redundancy resolution and optimization implementation. • Implementation into and analysis GUI and simulation framework Michael J. Del Signore December 16th 2005 Slide 17 of 57

  18. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Model Set Up • Assumptions • Planar • Skull and mandible are rigid bodies. • The skull is attached to the mandible via a revolute joint. • Muscle act along the line of action joining the origin and insertion points. Michael J. Del Signore December 16th 2005 Slide 18 of 57

  19. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Model Set Up • Coordinate Frames • (Xo, Yo) Inertial Frame: • Fixed in Space • Main Calculation Frame • (XU, YU) Upper Jaw Frame: • Attached to Skull (Upper Jaw) • Related to Inertial Frame through jaw gape angle q. • (XE, YE) End Effector Frame: • Created with the application point of the external/ desired or bite force. Michael J. Del Signore December 16th 2005 Slide 19 of 57

  20. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Screw Theoretic Modeling • Each muscle is modeled as a Revolute-Prismatic-Revolute (RPR) serial chain manipulator with an actuated prismatic joint. • An external (desired bite) force is applied to the system. • Need to calculate the actuator (muscle) forces needed to produce the external bite force. Michael J. Del Signore December 16th 2005 Slide 20 of 57

  21. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Screw Theoretic Modeling • Calculate end-effector twist generated by every serial chain present in the system. RPR Chains (Muscles) Revolute Jaw Joint Serial Chain Jacobian matrix whose column vectors represent the unit screws associated with each joint in the ith RPR serial chain. Unit screw created by the jaw joint. Michael J. Del Signore December 16th 2005 Slide 21 of 57

  22. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Screw Theoretic Modeling • Unit screws • Revolute Joints • Unit Screw with a pitch of zero (l = 0) • Prismatic Joints • Unit Screw with a pitch of infinity (l =∞) Upper Revolute Joint Lower Revolute Joint Jaw Revolute Joint Prismatic Joint Michael J. Del Signore December 16th 2005 Slide 22 of 57

  23. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Screw Theoretic Modeling • Unit screws Unit Direction Vectors Distance Vectors Michael J. Del Signore December 16th 2005 Slide 23 of 57

  24. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Screw Theoretic Modeling • Combine and generate the Jacobian matrices corresponding to every serial chain in the system – and simplify to 2-dimensions. RPR Serial Chains (Muscles) Jaw Joint Michael J. Del Signore December 16th 2005 Slide 24 of 57

  25. Modified Jacobian, in-active joints only. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Screw Theoretic Modeling • Reciprocal Wrench Formulation • Calculate the Selectively-Non-Reciprocal-Screws (SNRS) associated with the active joints (prismatic) in every serial chain. • SNRS – a screw which is reciprocal to all screws except the given screw. Prismatic Joint Formulation Jaw Joint Formulation • WP,i is the SNRS to the unit screw corresponding to the Pi joint that satisfies: Michael J. Del Signore December 16th 2005 Slide 25 of 57

  26. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Screw Theoretic Modeling • fP – Particular Solution • Equilibrating force field • Least-squares solution • fH – Homogeneous Solution • Interaction force field • Used to ensure that all muscle forces are acting in the same direction. • System Equilibrium Equation • Collect all SNRS’s – Prismatic Joints and Jaw Joint. • Redundancy Resolution • Pseudo-Inverse Solution Pseudo-Inverse of W Michael J. Del Signore December 16th 2005 Slide 26 of 57

  27. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Muscle Optimization • Muscles produce force in only one direction (contraction). • Implemented optimization routines minimize muscle forces while constraining them to remain positive (unidirectional) • Two optimization routines are developed and implemented. • Muscle Force Optimization • Muscle Activity Optimization Michael J. Del Signore December 16th 2005 Slide 27 of 57

  28. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Muscle Force Optimization Rank deficient • Find the full rank null space component of the system. • Singular-Value-Decomposition of H • r – Number of columns of S containing non-zero singular values. Design Variables Michael J. Del Signore December 16th 2005 Slide 28 of 57

  29. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Muscle Force Optimization • Pseudo-Inverse Solution • Separate Solution Components • Force Optimization Jaw Joint Reaction Forces Actuator (Muscle) Forces Michael J. Del Signore December 16th 2005 Slide 29 of 57

  30. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Muscle Activity Optimization • System Equilibrium Equation (Activity) Muscle Force • Normalized Muscle Activity Maximum Muscle Force • Muscle/ reaction forces in terms of activity. • Pseudo-Inverse Solution Michael J. Del Signore December 16th 2005 Slide 30 of 57

  31. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Muscle Activity Optimization • Pseudo-Inverse (Activity) Solution • Separate Solution Components • Activity Optimization Jaw Joint Reaction Activities • Forces Actuator (Muscle) Activities Michael J. Del Signore December 16th 2005 Slide 31 of 57

  32. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Implementation into a MATLAB Graphical-User-Interface (GUI) • Analysis GUI - Computational Simulation Tool • Uses the screw-theoretic model as a basis. • Parametrically analyze the muscles forces associated with an applied desired bite force. • User specifies the magnitude and location of the applied desired bite force and the location or location range of four separate muscles. • GUI calculates the muscle forces needed to produce the applied bite force. Michael J. Del Signore December 16th 2005 Slide 32 of 57

  33. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion MATLAB Analysis GUI • Mode2 Results - Stepped Static • Applied Force Definition • Mode Selection • Muscle Location Definition • Muscle Range Definition • Mode1 Results - Single Static • Optimization and Plot Options • Jaw Gape Definition Michael J. Del Signore December 16th 2005 Slide 33 of 57

  34. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion GUI Solution Validation • System Set Up • One Active Muscle • D.O.F = nm • Solved Analytically • Analytic Solution Michael J. Del Signore December 16th 2005 Slide 34 of 57

  35. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion GUI Solution Validation Michael J. Del Signore December 16th 2005 Slide 35 of 57

  36. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Virtual Model Simulation and Analysis Framework • Simulation of the simplified (2D) representation of the Smilodon musculoskeletal system. • Implemented within Simulink and VisualNastran. • Screw-Theoretic Model – main solution engine. • Basis for real-time control/ hardware-in-the-loop (HIL) simulation of a mechanical model of the system. Michael J. Del Signore December 16th 2005 Slide 36 of 57

  37. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Data / Information Flow Michael J. Del Signore December 16th 2005 Slide 37 of 57

  38. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion User Inputs • Desired Jaw Gape Angle Curve • Jaw gape angle over time • Simulation Time Michael J. Del Signore December 16th 2005 Slide 38 of 57

  39. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion User Inputs • Desired Bite Force Curve • Bite Force with respect to upper jaw over time Michael J. Del Signore December 16th 2005 Slide 39 of 57

  40. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion User Inputs • Initial Muscle Locations at q(0) & Maximum Forces • Block also serves as the link to the screw-theoretic model/ optimization (activity) routine. • Optimization feasibility check • Provides muscle (actuator) forces to VisualNastran model. Screw-Theoretic Model/ Activity Optimization Michael J. Del Signore December 16th 2005 Slide 40 of 57

  41. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion VisualNastran Simulink Block • Dynamic in-the-loop link between Simulink and VisualNastran. Michael J. Del Signore December 16th 2005 Slide 41 of 57

  42. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion VisualNastran Model • Two-Dimensional representation of the skull/ mandible musculoskeletal system. Michael J. Del Signore December 16th 2005 Slide 42 of 57

  43. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion VisualNastran Model • Measure Bite Force • Check for compatibility with applied bite force Michael J. Del Signore December 16th 2005 Slide 43 of 57

  44. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Framework Simulations • Four simulations • Identical Simulation Parameters – tmax, Dt, … etc • Varying/ Constant Jaw Gape • Varying/ Constant Bite Force Michael J. Del Signore December 16th 2005 Slide 44 of 57

  45. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Simulation 1 – Constant Angle/ Constant Force • Angle - 30° Force - 1000N Michael J. Del Signore December 16th 2005 Slide 45 of 57

  46. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Simulation 2 – Constant Angle/ Varying Force • Angle - 30° Force - 1000N to 500N Michael J. Del Signore December 16th 2005 Slide 46 of 57

  47. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Simulation 3 – Varying Angle/ Constant Force • Angle - 30° to 0° Force - 1000N Michael J. Del Signore December 16th 2005 Slide 47 of 57

  48. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Simulation 4 – Varying Angle/ Varying Force • Angle - 30° to 0° Force - 1000N to 500N Michael J. Del Signore December 16th 2005 Slide 48 of 57

  49. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Simulation Summary • Error peaks occur at same time. • Simulation Settling. • Rotation of arbitrary material. Michael J. Del Signore December 16th 2005 Slide 49 of 57

  50. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Design of a Mechanical Bite-Testing Prototype • Designed to simulate biting actions of various large felines • Accepts various dentition castings – adjustable. • Initial design developed for manual operation – with eventual implementation of computer control (HIL simulations) • Currently in preliminary manufacturing stages. Michael J. Del Signore December 16th 2005 Slide 50 of 57

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