A person is doing knee extension exercise by lifting a heavy object. At this moment, the leg is holding still. The weight of the lower leg is $\backslash (\backslash$mathrm$\{$W$\}\_\{0\}=200\backslash$mathrm$\{$~N$\}\backslash )$ and the weight of the heavy object is $\backslash (\backslash$mathrm$\{$W$\}\_\{1\}=300\backslash$mathrm$\{$~N$\}\backslash ).$ The object contacts foot at point A $,$ while the center of mass of the lower leg is point B $.$ Knee joint center is point O $.$ Muscle force generated by the knee extensors is exerted at point C through the patella tendon, with the force direction is $\backslash (\backslash$alpha$=30^\{\backslash$circ$\}\backslash )$ with the vertical. The distances between $\backslash ($ O $\backslash )$ and the application line of the muscle force, weight of the lower leg, and weight of the heavy object are $\backslash ($ d$\_\{$C$\}=4\backslash$mathrm$\{$~cm$\},$ d$\_\{$B$\}=10\backslash$mathrm$\{$~cm$\}\backslash ),$ and $\backslash ($ d$\_\{$A$\}=25\backslash$mathrm$\{$~cm$\}\backslash ),$ respectively.

$1)$ Calculate the joint reaction force of the knee joint and the magnitude of muscle force for keeping this posture; and

$2)$ Assuming the muscle force exerted on the patella bone by knee extensors is horizontal and point left, calculate the magnitude of contact force between patella and femur; and

$3)$ If there is no patella bone, the muscle force will increase or decrease? Why?

$($Please draw proper free body diagrams and write down assumptions if any$)$