High heart rate and calorie expenditure do not have a linear relationship - for example, my friend has a resting heart rate of around 90 (not good). He therefore should be burning far more calories than me at rest but that isn't the case. I would argue that calorie expenditure is also directly related to the recruitment of muscle fibres in a particular exercise that dictates how many calories are 'burnt'.
Thus, metabolic conditioning circuits (like the one I mentioned) can be very effective as 'cardio' workouts as you are recruiting lots of muscle fibres and demanding a pulmonary response to compensate for that.
I think this thread has gone off topic though - the original question asked whether it was possible to burn lots of calories at home with no equipment and YES, IT IS.
I don't like ellipticals for the following reasons:
1. The calorie readings on them are, at best, guesses.
2. Biomechanically, they produce a movement that is unnatural in humans.
3. Impact, even low/moderate, is important in exercise. Lack of impact contributes to all manner of injuries and osteoporosis.
Point taken re: muscle helps to burn calories but you have to take time to build that muscle, its not going to be burning an awful lot right away and it could take a while whilst you bulk up the muscle to lose the fat. I assumed the OP wanted fairly fast results which is why I suggested cardio. Muscle building stuff goes without saying but can often be created as a direct result of cardio under resistance (eg running up hill, spinning under high resistance or ...the elliptical machine with high intensity).
See, where I stand on the Elliptical (cross trainer) machines is that they do get me a high heart rate- I don't buy the calorie readings on ANY machine- not even my heart rate monitor though would expect its a more consistant result (even if they all do exaggerate.) Hence I watch my heart rate, not my calorie burn. I aim for machines which get my heart rate as high as I can. This used to include running but I have shin problems which I wont rest (know I should but can't let myself! It would take months to repair, I tried a fortnight and it made no difference). I have problems therefore with any high impact exercise. I can run up hills and its just about OK but running flat causes me too much pain. Hence the reason the elliptical machine is very useful. Its exactly because its no/low impact. Agree elliptical machines are not helpful in aiding a natural movement, I don't use only the machine for my workouts, I use about 10 different machines and occasionally run outside (-although I pay for it for about a fortnight after!). Any machine used by itself wouldn't be advised I think. Not just the elliptical machine. (They are great for HIIT though!)
Look, I have been told I have osteoperosis of the spine. (this is partly genetic and partly due to an eating disorder I had 10 years ago which never fully recovered because I cut out dairy because I am intollerant-doctor checked.)
I have been told my legs are fine as a result of the exercise I do which is no/low impact and 80% of the time based on my legs doing all the work.
I was told its more of a 'use-it-or-lose-it' thing when it came to osteoperosis and exercise, not so much about impact which can even cause pain and fractures if you do have osteoperosis (google horse riding and osteoperosis!)
Anyway, back to the topic!
I was thinking today that your replies reminded me of a personal trainer I once met. He was all for muscle work and dead against any cardio what so ever claiming cardio was pointless.
Now I am not saying you are from the same school of thought as he is, but its safe to say there are different schools of thought, different opinions and different ways of doing things perhaps? maybe a good idea is for the OP to do a little of everything and see what works. It would seem if there are different proven ways to do things that each would suit a different person and its about finding what works for that person.