Chair Yoga Pose (Utkatasana or "Fierce Pose") is like doing a half squat.
As you move your hips back bend your knees and tilt your pelvis and ribcage forwards. So that you can keep your heels on the floor as you bend your knees, move your pelvis and knees back relative to your feet.
Work at keeping the pressure even on the fronts of your feet and your heels so that you stay balanced in this yoga pose. To that end it can help to reach your ribcage forwards. You can also reach your arms forwards.
Normally utkatasana is taught with the feet together. If you are just getting used to this yoga pose, or if you have knee problems, you might want to do it with feet hip width (or a comfortable distance) apart.
To make lifting your arms easier, reach your shoulders forwards first. This activates the serratus anterior muscle. Then reach your arms forwards and up while keeping your shoulder blades spread. Start of with your hands shoulder width and try squeezing them towards each other each time you inhale. If you can get them together easily then keep them together.
While trying to bring your arms together focus on reaching them upwards. To make this easier, reach your shoulders upwards while keeping your shoulder blades spread. This action uses the trapezius muscle.
The first part of protecting your knees is learning to feel them and be aware of them while they are pain free.
So that it is easier to feel your knees practice moving in and out of chair yoga pose slowly and smoothly. An advantage of moving slowly is that you can stop easily if you do notice pain. You can then make adjustments to the way that you do the pose.
To protect your knees in utkatasana the most important thing you can do is focus on feeling your knees. If you focus on feeling your knees you can change the way that you do utkatasana if you notice sharp pain or discomfort in your knee joints.
One of the simplest things that you can do to protect your knees is to keep them pointing in the same direction as your toes. To do this you have to be aware both of your feet and your knees.
You can fine tune this relationship by pointing your knees either at your second toe or third toe.
I often do and teach chair yoga pose by reaching the hips back so that both the hips and knees move backwards. The idea of this was to prevent the knees from going to far forwards. However I later found that on occasion when I had knee pain the solution was to move my hips and knees forwards.
This is why it is important that you focus on feeling your knees (and the rest of your body.) If you feel pain you can make adjustments to make your knees alleviate the pain now.
In a section below I talk about adjusting the position of the spine. This too can have an affect on the knees and knee pain. To adjust the "shape" of your spine try curving it backwards or forwards or try straightening it. You may find that this sometimes helps.
Solving knee pain generally isn't a simple process. One of the things that I am currently working with to help with knee pain in chair pose is activating the sides of the thighs and hips. The muscles activated can include the vastus lateralis (side of the thighs), gluteus minimus, gluteus medius and tensor fascae latae (side of the hips).
To activate these muscles focus on creating a squeezing sensation at the side of the thighs and hips. Then try to vary and move the squeezing sensation, noticing any affects on your knees.
While doing this action, keep your knees pointing in the same direction as your toes. Your inner thigh muscles (adductors) will then more than likely automatically activate to counter act the action of your outer thigh and hip muscles activating.
You can also experiment with moving or expanding the "squeezing" sensation to include the back of the thighs. For myself I find that I can create a "squeeze" just above the backs of the knees. However this may depend on the amount of knee bend that you have.
That may also be another solution to knee pain, change the amount of bend in your knees. That can mean moving your knees forwards or backwards to change the amount of knee bend. It can also mean changing how high or low you go in chair pose. The ideal is to have a complete range of motion in your knees, however if you have pain, then slowly work at extending your range of motion. Stay the pain-free side of your range of motion and see if you can slowly work at expanding your range of motion.
Another point is to be aware of your feet. Activate them when doing chair yoga pose. Press down through the root of the big toe, the point at the front of the foot just before the big toe. Lift the center of your inner arch also. (Though this may already be lifted if your knees are pointing in the same direction as your toes.) You can also try pressing down through the front of the foot just behind the little toe.
If you are activating the sides of your thighs you may find that when you also activate your feet your feet feel very strong and stable.
One reason for activating the feet and ankles, is that doing so stabilizes the shins. Muscles that cross the knee joint then have a stable foundation to work from.
Another way to give muscles of the knee a stable foundation is to make your hip joints stable.
When doing utkatasana you could focus on bending your spine backwards or straightening it. To bend your spine backwards you'll have to tilt your pelvis forwards. To bend your spine forwards you'll have to tilt your pelvis back.
Tilting your pelvis back to straighten your spine you may find, if you pay attention to your lower back, a position when your lower back feels open and comfortable. It's quite a pleasant feeling. To find this position tilt your pelvis back slowly. Stop when you feel your lower back feel open.
Bending your spine backwards you can cause your spinal erectors to engage.
If you are going to use your spinal erectors to bend your spine backwards, see if you can also use them to "flick" your tailbone backwards and upwards. You may feel a "pull" at the back of your sacrum as you do this.
After pulling your tailbone back you can then activate your pubococygeus and try pulling it forwards towards your pubic bone while keeping your spinal erectors active. While doing this you may feel some of your deeper hip muscles activating (maybe piriformins, obturator internus, gemellus superior and inferior and quadratus femoris.)
One of the challenges of chair yoga pose is to lift up even though you are sinking down. Focus on lifting your ribs and arms (and head) away from your pelvis.
This can be helpful if you have knee pain since lifting the ribcage away from the pelvis adds tension to the midsection. This can help to provide a fixed foundation for muscles that attach from the pelvis and work on the knees.
You can practice moving your ribs away from your pelvis while standing. Work at keeping the same feeling as you bend your knees and sink your hips down. Reach your ribs and arms away from your pelvis as you sink your pelvis down.
You can turn this into a breathing vinyasa by lengthening your upper body as you inhale and relaxing while you exhale. Focus on moving your ribs, shoulders and arms up while you inhale and then on relaxing slightly while you exhale. You can also focus on lengthening your neck and on opening the top of your chest while you inhale.