There are many different muscles within the hand that work when different grips are used. When the pinch grip is being used the adductor pollicis is engaged. (See figure 1 for the muscle location) This muscle contracts and relaxes filling the web space between the index finger and thumb. Figure 1: Adductor Pollicis The support grip and crush grip uses 2 different muscles but both muscles are used in each grip, just the main muscle differs. When completing the support grip you flex the distant part of the finger by actioning the flexor digitorum profundus. (See figure 2 for the location of this muscle) Figure 2: Flexor Digitorum Profundus The crush grip requires action from the proximal part of the finger byt the movement of the flexor digitorum superficialis. (See Figure 3 for the location of the muscle) Figure 3: Flexor Digitorum Superficialis The support grip is stronger than the crush grip as the profundus muscle goes under and through the superficialis giving it greater leverage in movement. This can be seen through evolution as more hanging has been done rather than crushing.