A compound and push exercise, use the machine-assisted triceps dip to strengthen the muscles necessary to be able to perform the proper triceps dip.
Targeting your quadriceps, the jump squat (aka squat jump) is a brilliant compound bodyweight exercise with which you can develop lower-body power.
Targeting your erector spinae, use the flat bench hyperextension only if you do not have access to a hyperextension bench. The range of motion is limited.
Targeting your iliopsoas, not your abs, the captain's chair leg raise is a hip flexion exercise. Your abs and obliques act as important stabilizers.
The one-leg push-up, which targets your lower pecs and obliques, puts your body out of balance, thus forcing the recruitment of more stabilizer muscles.
For the twisting crunch, it’s important to fully relax your waist before each contraction to ensure that your muscles dynamically contract during each rep.
Target your hamstrings and obliques using the twisting hip extension, an isolation exercise. Your gluteus maximus and adductor magnus act as synergists.
Work your iliopsoas and other hip flexors using the lying alternating leg raise, an isolation exercise. Your abs and obliques only act as stabilizers.
In one classic study, the diamond push-up (aka triangle push-up) was found to be the most effective exercise for activating the triceps brachii!
Targeting your abs and obliques, the one-leg front plank is a unilateral bodyweight exercise useful for developing the strength and stability of your core.
Targeting the lower pectoralis major, the knee push-up is a brilliant exercise for beginners. Use it to build strength until you can do actual push-ups.
Targeting your iliopsoas, not your rectus abdominis, the lying straight leg raise is an isolation pull exercise that activates all hip flexor muscles.