Dr. Muller is at PetSmart buying kitty litter for his familys cats, Snooki, Pauly D, and Chipotle, and is walking to the checkout lines. A dog breaks free from its owner, and Dr. Muller pauses during walking to let the dog pass. Assume Dr. Muller is in a one-legged stance during gait as shown. Also assume the following:

The locations of the body center of mass (COM), knee, lower leg/foot COM, kitty litter COM, and ground reaction are marked with stars.

) with the horizontal.f), and the lower leg makes a 65 degree angle (q The knee is flexed at a 120 degree angle (

) with the tibia, and attaches 5cm distal to the tibio- femoral joint.g The patella tendon forms a 15 degree angle (

The quadriceps run parallel to the femur.

The patella acts as a frictionless pulley.

Dr. Muller weighs 700N.

Dr. Mullers COM is at the same x-coordinate as the ground reaction, but is 10cm posterior in the z-axis.

The lower leg and foot combined weigh 50N.

The lower leg/foot COM and the ground reaction have the same z-coordinate and the same x- coordinate.

The kitty litter weighs 100N, and is 25cm anterior and 15cm lateral to ground reaction.

The knee is 5cm anterior to the ground reaction in the z-axis, and has the same x-coordinate as the ground reaction.

The knee is 33cm above the ground reaction, and 18cm above the lower leg/foot COM.

Draw a free-body diagram of the tibio-femoral joint, and write out the system of equations that are necessary and sufficient to determine the magnitude of the quadriceps muscle force and any and all reactions at the tibio-femoral joint. DO NOT SOLVE THE SYSTEM OF EQUATIONS.