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

2. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 2 of 57 Agenda Introduction Background Case Scenario System Modeling GUI Implementation Simulation Framework Mechanical Prototype Design Future Work Conclusion

3. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 3 of 57 Motivation 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. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Computational advances in the past decade have revolutionized engineering!! Improved Infrastructure Advanced Algorithms and Methodologies

4. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 4 of 57 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. Integration and application of certain engineering principles and techniques into one of the candidate biological sciences fields: Musculoskeletal System Analysis Powerful Tool Three Critical Steps Model creation with adequate fidelity. Analysis of various actions/ behaviors. Iterative testing for refining hypotheses. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

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

6. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 6 of 57 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 Existing Tools Musculoskeletal System Analysis Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

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

8. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 8 of 57 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). Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

9. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 9 of 57 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] Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

10. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 10 of 57 Mathematical Preliminaries 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. Unit Screw - Unit vector pointing along the direction of the screw axis. - Moment of the screw axis about the origin. - Location of a point on the screw axis.  - Pitch, the ratio of translation to rotation. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

11. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 11 of 57 Mathematical Preliminaries 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. Twists (Velocity) Wrenches (Force) Linear Velocity Angular Velocity Applied Force Moment caused by F o Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

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

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

14. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 14 of 57 Simulation of Mechanical Smilodon Implemented using a prescribed motion analysis within VisualNastran Simulation was successful but more complexity was desired. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

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

16. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 16 of 57 Smilodon Virtual Prototype – VisualNastran Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion 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. 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.

17. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 17 of 57 Our Model Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion 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

18. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 18 of 57 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. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

19. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 19 of 57 Model Set Up Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Coordinate Frames (X o, Y o ) Inertial Frame: -Fixed in Space -Main Calculation Frame (X U, Y U ) Upper Jaw Frame: -Attached to Skull (Upper Jaw) -Related to Inertial Frame through jaw gape angle  (X E, Y E ) End Effector Frame: -Created with the application point of the external/ desired or bite force.

20. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 20 of 57 Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion 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. Screw Theoretic Modeling

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

22. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 22 of 57 Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Unit screws Revolute Joints Unit Screw with a pitch of zero ( = 0) Upper Revolute JointLower Revolute JointJaw Revolute Joint Screw Theoretic Modeling Prismatic Joints Unit Screw with a pitch of infinity ( =∞) Prismatic Joint

23. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 23 of 57 Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Unit screws Screw Theoretic Modeling Unit Direction Vectors Distance Vectors

24. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 24 of 57 Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion 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 Screw Theoretic Modeling

25. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 25 of 57 Screw Theoretic Modeling Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion 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 W P,i is the SNRS to the unit screw corresponding to the P i joint that satisfies:. -Modified Jacobian, in-active joints only. Jaw Joint Formulation

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

27. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 27 of 57 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 Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

28. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 28 of 57 Find the full rank null space component of the system. Singular-Value-Decomposition of H  – Number of columns of  containing non-zero singular values. Muscle Force Optimization Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Rank deficient Design Variables

29. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 29 of 57 Pseudo-Inverse Solution Separate Solution Components Muscle Force Optimization Jaw Joint Reaction Forces Actuator (Muscle) Forces Force Optimization Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

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

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

32. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 32 of 57 Implementation into a MATLAB Graphical-User-Interface (GUI) Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion 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.

33. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 33 of 57 MATLAB Analysis GUI Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Mode SelectionApplied Force Definition Muscle Location Definition Muscle Range Definition Jaw Gape Definition Optimization and Plot OptionsMode1 Results - Single Static Mode2 Results - Stepped Static

34. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 34 of 57 GUI Solution Validation Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Analytic Solution System Set Up One Active Muscle D.O.F = n m Solved Analytically

35. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 35 of 57 GUI Solution Validation Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

36. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 36 of 57 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. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

37. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 37 of 57 Data / Information Flow Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

38. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 38 of 57 User Inputs Desired Jaw Gape Angle Curve Jaw gape angle over time Simulation Time Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

39. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 39 of 57 User Inputs Desired Bite Force Curve Bite Force with respect to upper jaw over time Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

40. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 40 of 57 User Inputs Initial Muscle Locations at  (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. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Screw-Theoretic Model/ Activity Optimization

41. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 41 of 57 VisualNastran Simulink Block Dynamic in-the-loop link between Simulink and VisualNastran. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

42. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 42 of 57 VisualNastran Model Two-Dimensional representation of the skull/ mandible musculoskeletal system. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

43. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 43 of 57 VisualNastran Model Measure Bite Force Check for compatibility with applied bite force Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

44. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 44 of 57 Framework Simulations Four simulations Identical Simulation Parameters – t max,  t, … etc Varying/ Constant Jaw Gape Varying/ Constant Bite Force Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

45. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 45 of 57 Simulation 1 – Constant Angle/ Constant Force Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Angle - 30° Force - 1000N

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

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

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

49. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 49 of 57 Simulation Summary Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Error peaks occur at same time. Simulation Settling. Rotation of arbitrary material.

50. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 50 of 57 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. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

51. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 51 of 57 Dentition Castings CAD models developed from fossil records. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

52. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 52 of 57 Mechanism Adjustability Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion Ensure proper dentition location. Locks in place during use. Rotation Point Location Skull/Mandible Location

53. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 53 of 57 Mechanical Prototype – Force/ Torque Analysis GUI Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

54. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 54 of 57 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). Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

55. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 55 of 57 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. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

56. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 56 of 57 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. Introduction Background Case Scenario Simulation Mechanical Prototype Future Work Conclusion

57. Automation, Robotics, and Mechatronics LAB – SUNY Buffalo Michael J. Del Signore December 16 th 2005 Slide 57 of 57 Thank You Questions?