Kinetics Chapter 4 Dr Moran EXS 587 Tuesday November 12 2007 Lecture Outline Review Homework Assignmet Anthropometry Lecture Objectives Intro to Forces Newton s Laws Free Body Diagrams Moments Link Segment Model Measurement of Force 1 What is FORCE Represents the ACTION of one BODY on ANOTHER Field of Biomechanics Effect that a force has on a particle or perfectly rigid body Ex Necessary to understand the causes of motion use Newton s Laws Effect that a force has on a deformable body or material Ex Internal forces within biological soft tissues strain in the ACL during a cutting experiment Typically these forces need to be ESTIMATED or CALCULATED from measured kinematics FORCE con t F Characterized by Three Things Magnitude Direction Point of application where on the body is the force applied important when calculating moment What if the force is applied over a region or area PRESSURE force distributed over an area P Force Area http www laboratorium dist unige it piero Teaching Gait BONTRAGER 20Instrumented 20Gait 20Analysis 20Systems files INSOLE1 JPG 2 Moment Torque Def Force acting through a distance tending to cause rotation length F M F length Static Equilibrium In a static situation NO movement No acceleration F ma 0 y M x 3 Newton s Laws A Refresher from Physics Isaac Newton 1687 Philosophiae Naturalis Principia Mathematica Laws define relationship between force and linear motion of a rigid particle Law of Inertia a body will remain in its current state of motion unless acted upon by an external force P momentum mv Law of Acceleration the force will cause the body to accelerate in direct proportion to the magnitude of the force and in the same direction as the force F ma Law of Reaction when one body applies a force to another body the second body applies an equal and opposite reaction force on the first body Ex Ground Reaction Force Free Body Diagrams FBD Multiple Forces Acting at One Time Can be replaced by one RESULTANT force which is the summation of all forces acting on the body A FBD is a sketch of the rigid body showing the forces acting on that body Always the first step in solving a STATIC mechanics problem Static not moving no accelerations 4 Steps for constructing a FBD 1 Draw a simple sketch of the rigid body of interest 2 Write out coordinates of segment to define its position if known 3 Indicate COM of segment 4 Draw all known forces and moments with directions indicated 5 Draw all unknown forces and moments Joint Contact Force What contributes to contact forces at joints Soft tissue components muscle ligaments crossing the joint Bone bone contact For a simple activity as standing on one leg the forces at the hip joint can be attained using a four step approach 1 2 3 4 Isolate joint of interest and identify opposing bones and structure Draw a FBD Write equations of STATIC equilbrium Solve 3 equations and 3 unknowns 5 Joint Forces Example Isolate Joint of Interest Identify opposing bone structures Draw FBD Write equations of static equilibrium B a2 b a1 A J Joint Forces con t Decompose forces into x and y components a2 b a1 Ax Jy J A Ay A Jx J Write equations of static equilibrium FX 0 FY 0 CCW MHJ 0 6 Trigonometry Review sin Fy F Fy cos Fx F F Fy F cos Fy F sin Fx Fx F sin Fx F cos F Fy2 Fx2 1 2 B a2 Joint Forces con t b a1 Ax Jy J A J Ay A Jx Write equations of static equilibrium FX 0 Acos Jcos FY 0 Jsin Asin B MHJ 0 B b Acos a1 Asin a2 THREE EQUATIONS THREE UNKNOWNS 7 Link Segment Model Assumptions 1 Each segment has a fixed mass located as a point mass at its COM 2 COM location fixed 3 Joints are considered as hinges 4 Mass MOI about its COM is fixed during movement 5 Segment length fixed Anatomical Model Link Segment Model Example 1 Calculate the abductor muscle force and the hip joint reaction force for a male and a female standing on one leg Assume the following dimensions B a2 a1 14cm a2 4cm b 20cm MALE b 22cm FEMALE 80o b a1 A J See Solution Handout 8 5000 Abductor male 4500 Abductor female Abductor Force N 4000 3500 3000 2500 2000 1500 1000 500 0 444 5 555 7 666 8 777 9 889 0 1000 2 1111 3 1222 4 1333 6 Body Weight N 7000 Joint Reaction Force male 6000 Hip Joint Rx Force N Joint Reaction Force female 5000 4000 3000 2000 1000 0 444 5 555 7 666 8 777 9 889 0 1000 2 1111 3 1222 4 1333 6 Body Weight N 9 Joint Reaction Force vs Bone on Bone Force Case 1 bone on bone force is 0 Case 2 bone on bone force is 70N compression In both cases the lower segment acts downward with 100N Acting across the joint space notice the reduced joint space Example 2 In a static situation a person is standing on one foot on a force plate The ground reaction force is found to act 4 cm anterior to the ankle joint The subject s mass is 60 kg and foot length is 12 cm Calculate the joint reaction forces and net muscle moment at the ankle Ry M Rx 6 4 GRF Foot Mass 10 Course Outline From Static to Dynamic What changes Measurement of Force What devices to use Operating Principles of the Force Plate Combined Force Plate and Kinematic Data Lab Experience Collecting Force Plate Data Inverse Dynamics External Forces Distal Forces Moments Motion Newton Euler Equations Proximal Forces Moments 11 Standing Still What forces are active When standing still your weight vector is seeking to accelerate you downward at 9 81 m s2 The person does NOT accelerate downward because the ground exerts an equal and opposite force upward W Fg W Fg 0 Fg ground reaction force What if it is not a static situation Fx max Fy may M Io Example 3 con t from last lecture From the data collected during the swing of the foot calculate the muscle moment and reaction forces at the ankle The subject s mass was 80 kg and the anklemetatarsal length was 20 0 cm Use Table 3 1 to calculate the inertial characteristics of the foot Table 3 1 Calculations m 0 0145 80 1 16 kg po 0 475 0 20 0 095 m Io 1 16 0 095 0 0105 kg m2 12 Example 3 continued Ry M Measured Kinematics Accelerations of Center of Mass Rx Ax 9 07 m s Ay 6 62 m s2 21 69 rad s Distances From Ankle Joint to Center of Mass What are we solving for FW Ankle Joint Reaction Force Muscle Moment about Ankle Joint Solution see handout Example 4 For the same instant in time calculate the muscle moments and reaction forces at the knee joint The leg segment is 43 5 cm long 13 Ways to Measure Force Transducers Force …