Musculoskeletal simulation is the powerful tool to analyze the human motion and provide related information such as muscle activities and reaction force in the joints. It has been successfully applied to the fields of surgery, rehabilitation, and ergonomics. However, most of the models assume the articulations as the standard mechanical joints such as spherical and revolute joints. Although these joints can provide good approximation of the articulations, they cannot exactly simulate the motions of the articulations and provide correct data such as slippage and reactions among femur, tibia and patella in the knee articulation. In addition, the effects of ligaments are totally ignored. The cruciate ligaments are very important to stabilize the knee. Injury on cruciate ligaments, especially anterior cruciate ligament, happens very often on athletes who play intense sports, and it is almost impossible to recover to its original state. In order to study the effect of ligaments in knee articulation, both conditions of force and moment equilibrium and contact engagement analysis are utilized in the planar model presented in this paper. The motion of quasi-static stand-to-sit is studied based on the method. The results also show the consistent with previous studies. In addition to the effect of ligaments, this method also provides a computational method for the contact conditions among femur, tibia, and patellar. This problem was studied by comparing the distance of discrete points on the femoral condyle surfaces. Therefore, it costs a lot of computing time. With the method of contact analysis, which was developed in gear theory, solutions can be obtained faster and more accurate.