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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2008/
Module Title: Biomechanics
Module Code: BIOE
School: Mechanical and Process Engineering
Programme Title: Bachelor of Engineering in Biomedical Engineering
Programme Code: CR_EBIME_7_Y
External Examiner(s): Mr. Murtagh Murphy, Dr. Garrett McGuiness Internal Examiner(s): Dr. Keith Bryan
Instructions: Attempt 4 questions (all questions carry equal marks)
Duration: 2 Hours
Sitting: Winter 2008
Requirements for this examination:
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
- Consider a person standing on one tiptoe. The forces acting on the foot during this instant are shown in Figure Q1. W is the person's weight applied on the foot as the ground reaction force, Fm is the magnitude of the tensile force exerted by the gastrocnemius and soleus muscles on the calcaneus through the Achilles tendon and Fj is the magnitude of the ankle joint reaction force applied by the tibia on the dome of the talus. The weight of the foot is small compared to the weight of the body and is therefore ignored. The Achilles tendon is attached to the calcaneus at A, the ankle joint centre is located at B, and the ground reaction force is applied on the foot at C. For this position of the foot, it is estimated that the line of action of the tensile force in the Achilles tendon makes an angle θ with the horizontal, and the line of action of the ankle joint reaction force makes angle β with the horizontal. Assuming that the relative positions of A, B, and C are known. (a) Determine expressions for the tension in the Achilles tendon and the magnitude of the reaction force at the ankle joint. (14 marks) (b) Calculate the Joint and Muscle forces when θ= 45º and β= 60º. (6 marks)
- The following observations were taken from a test on a shaft when transmitting power: Shaft material: Mild steel (G = 80 × 10^3 N/mm^2 ) Diameter of shaft: 75mm Length under test: 15m Total angle of twist: 20 ˚ Speed of rotation: 280 rev/min. Calculate: (i) the maximum stress in the shaft. (7 marks) (ii) the maximum torque transmitted. (7 marks) (iii) the power transmitted. (6 marks)
Figure Q1 Forces on the ankle
- Consider the rectangular bar shown in figure Q5 with original (undeformed) dimensions a = b = 2 cm and c =20cm. The elastic modulus of the bar material is E =
100 GPa and its Poisson’s ratio is υ = 0.3. The bar is
subjected to biaxial forces in the x and y directions such that Fx = Fy = 0.4 x 10^6 N and that Fx is tensile while Fy is compressive. Assuming that the bar material is linear elastic, determine: (i) The average normal stresses σx , σy, and σz developed in the bar (6 marks) (ii) The average normal strains εx , εy, and εz (9 marks) (iii) Dimension, c’ ,.of the bar in the x-direction after deformation (5 marks)
Figure Q
