Answer:
The contraction you are referring to is most likely the concentric contraction of the quadriceps muscles in the front of the thigh, as well as the gluteus maximus muscle in the buttocks, as you push off the lower step and lift your body up to the next step. These muscles work together to extend the knee and hip joints, generating the force necessary to lift the body weight against gravity.
Additionally, the calf muscles, specifically the gastrocnemius and soleus muscles, are also involved in this movement to some extent, as they contract to help stabilize the ankle joint and provide additional push-off force.
It's important to note that climbing stairs is a complex movement that involves multiple muscle groups working together, and the specific muscles involved may vary depending on the individual's movement patterns and technique.