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A Screw-Theoretic Framework for Musculoskeletal Modeling and Analysis Michael J. Del Signore ([email protected]) December 16th 2005 Advisor: Dr. Venkat Krovi Mechanical and Aerospace Engineering State University of New York at Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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. Powerful Tool and • Integration and application of certain engineering principles • Analysis of various actions/ behaviors. techniques into one of the candidate biological sciences fields: • Iterative testing for refining hypotheses. Musculoskeletal System Analysis Michael J. Del Signore December 16th 2005 Slide 4 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Challenges • Unlike traditional engineering systems, musculoskeletal systems inherently possess considerable irregularities redundancies. Irregularities andRedundancies • Complex Asymmetric Geometric Shapes (i.e. muscle, bone). • Multiple Muscles: More actuators than degrees of freedom. • Dealing with (trying to simulate) living tissue. effector force. •• Each Musculoskeletal analysis tools need• to take these characteristics Infinite set of actuator (muscle) specimen is unique. into account. forces can produce the same end- Michael J. Del Signore December 16th 2005 Slide 5 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 … • 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 • Physics, Dynamics, FEA, Contact, Friction – Implementation into real-time control frameworks Michael J. Del Signore December 16th 2005 Slide 6 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Michael J. Del Signore December 16th 2005 Slide 7 of 57 Rapid Real-Time Simulation and Analysis Relatively Impossible Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Mathematical Preliminaries • Screw Coordinates Unit Screw uˆ - Unit vector pointing along the direction of the screw axis. v uˆ 0 = r ´ uˆ + l uˆ - Moment of the screw axis about the origin. v r - Location of a point on the screw axis. l - Pitch, the ratio of translation to rotation. 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Mathematical Preliminaries • Screw Coordinates Twists (Velocity) Linear Velocity 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Michael J. Del Signore December 16th 2005 Slide 13 of 57 Virtual Recreation Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Smilodon Virtual Prototype – VisualNastran • Constraints were placed on the system to represent: • The simulation was met with limitations: • Muscles Linearin Actuators • Due to the software's inability to handle redundancy terms of resolving the multiple muscle forces an inverse • in Skull/ Mandibledynamics Interaction setting. Revolute Joint • These shortcomings provided the motivation for the development of our own low-order computationally tractable model based on screw-theoretic methods. • External forces (or alternately a prescribed motion) was applied to the skull as userspecified input to the system. Michael J. Del Signore December 16th 2005 Slide 16 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 • (XE, YE) End Effector Frame: • (XU, YU) Upper Jaw Frame: - Attached to Skull (Upper Jaw) - Related to Inertial Frame through jaw gape angle q. - Created with the application point of the external/ desired or bite force. Michael J. Del Signore December 16th 2005 Slide 19 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Screw Theoretic Modeling • Unit screws • Prismatic Revolute Joints Joints • Unit Screw with a pitch of infinity zero (l =(l0)=∞) Upper Revolute Prismatic Joint Joint Michael J. Del Signore December 16th 2005 Slide 22 of 57 Lower Revolute Joint Jaw Revolute Joint Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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) Michael J. Del Signore December 16th 2005 Slide 24 of 57 Jaw Joint Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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: J%i - Michael J. Del Signore December 16th 2005 Slide 25 of 57 Modified Jacobian, in-active joints only. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Screw Theoretic Modeling • System Equilibrium Equation • Collect all SNRS’s – Prismatic Joints and Jaw Joint. fP – Particular Solution • Equilibrating force field • Least-squares solution fH – Homogeneous Solution • Interaction force field • Redundancy Resolution • Pseudo-Inverse Solution • Used to ensure that all muscle forces are acting in the same direction. Pseudo-Inverse of W Michael J. Del Signore December 16th 2005 Slide 26 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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. | | | v v # S U1 U 2 Ur ¢ f = W $W + S ν | | | Design Variables Michael J. Del Signore December 16th 2005 Slide 28 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Muscle Force Optimization • Pseudo-Inverse Solution • Force Optimization • Separate Solution Components Jaw Joint Reaction Forces fo21 fPo21 So 2r ν r 1 fmnm 1 fPmnm 1 Sm nm r Actuator (Muscle) Forces Michael J. Del Signore December 16th 2005 Slide 29 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Muscle Activity Optimization • Normalized Muscle Activity Muscle Force • System Equilibrium Equation (Activity) Maximum Muscle Force • Muscle/ reaction forces in terms of activity. Michael J. Del Signore December 16th 2005 Slide 30 of 57 • Pseudo-Inverse Solution Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Muscle Activity Optimization • Pseudo-Inverse (Activity) Solution • Activity Optimization • Separate Solution Components Jaw Joint Reaction Activities fo f So Po ν fm fPm Sm • Forces Actuator (Muscle) Activities Michael J. Del Signore December 16th 2005 Slide 31 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion MATLAB Analysis GUI Mode2 Stepped Static Mode Selection Force Definition • Applied Muscle Location Range Definition Definition Mode1 Optimization Results and - Single Plot Options Static Jaw Gape Definition Michael J. Del Signore December 16th 2005 Slide 33 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion GUI Solution Validation Michael J. Del Signore December 16th 2005 Slide 35 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Data / Information Flow Michael J. Del Signore December 16th 2005 Slide 37 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Simulation 1 – Constant Angle/ Constant Force • Angle - 30° Michael J. Del Signore December 16th 2005 Slide 45 of 57 Force - 1000N Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Simulation 2 – Constant Angle/ Varying Force • Angle - 30° Michael J. Del Signore December 16th 2005 Slide 46 of 57 Force - 1000N to 500N Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Simulation 3 – Varying Angle/ Constant Force • Angle - 30° to 0° Michael J. Del Signore December 16th 2005 Slide 47 of 57 Force - 1000N Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Simulation 4 – Varying Angle/ Varying Force • Angle - 30° to 0° Michael J. Del Signore December 16th 2005 Slide 48 of 57 Force - 1000N to 500N Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo 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 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Dentition Castings • CAD models developed from fossil records. Michael J. Del Signore December 16th 2005 Slide 51 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Mechanism Adjustability • Ensure proper dentition location. • Locks in place during use. Skull/Mandible Location Rotation Point Location Michael J. Del Signore December 16th 2005 Slide 52 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Mechanical Prototype – Force/ Torque Analysis GUI Michael J. Del Signore December 16th 2005 Slide 53 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Future Work • Completion of Mechanical Prototype • Implementation of cable-actuation strategy – simulating muscles. • Implementation into real-time HIL control analysis framework. • Extension Screw-Theoretic Model to Three-Dimensions • Higher degree of complexity and realism. • Additional analysis GUI. • Provide modeling and solution basis for HIL simulations. • Implementation of Muscle Physiological Properties • Max muscle force currently only property considered. • Insight into what types of muscles are needed to produce desired bite force. • Preliminary inclusion of physiological muscle properties explored using Virtual Muscle (Simulink muscle model). Michael J. Del Signore December 16th 2005 Slide 54 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Conclusions • Application of existing tools to musculoskeletal system analysis was explored. • Traditional engineering tools found inadequate at handling inherent system redundancies. • Specific musculoskeletal modeling tools require a high amount modeling detail and application specific programming – rapid real-time simulation and analysis relatively impossible. • Developed a screw-theoretic framework for modeling and analyzing the skull/mandible musculoskeletal system of a saber-tooth cat. • Modeled as a redundantly actuated parallel manipulator. • Framework resolves muscle forces needed to produce a desired bite force. • Redundancy resolution scheme implemented a typical pseudo-inverse solution methodology. • Muscle force and activity optimizations were explored and implemented. Michael J. Del Signore December 16th 2005 Slide 55 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Conclusions • Screw-Theoretic Framework provided the basis for the development of a MATLAB analysis GUI • Parametrically analyses the muscle forces or activities (four muscle) needed to produce a desired bite force. • Virtual simulation framework developed. • Simulated a virtual representation of the saber-tooth cat. • Implemented within Simulink and VisualNastran. • Measured bite force compared to the applied bite-force. • Overall the simulation was successful. • Introduced a mechanical bite-testing prototype. • Perform bite testing simulations on various large felines. • Basis for implementation into real-time HIL analyses. • Overall the developed screw-theoretic modeling and analysis framework shows significant promise at speeding up the musculoskeletal system analysis processes. Michael J. Del Signore December 16th 2005 Slide 56 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Thank You Questions? Michael J. Del Signore December 16th 2005 Slide 57 of 57 Automation, Robotics, and Mechatronics LAB – SUNY Buffalo