Elliptical machines are designed especially to minimize potential injuries from impact and stress on the joints. As with any workout, there are risks, particularly if you have been injured in the past or are in poor health. But the concept behind elliptical machines is to minimize this risk.
Ellipticals work to mimic the cardio-vascular benefits of running or jogging, while eliminating joint impact and stress. Some users of ellipticals have reported injury, but most of these are actually aggravation of a previous injury or pre-existing condition.
Running provides wonderful aerobic exercise and cardio-vascular workout. But the strain on your knees, ankles, and even hips can cause permanent damage. Ellipticals allow you to achieve these aerobic goals without having to worry about sprains or ligament tears.
Additionally, when you use an elliptical, you get a more complete workout than running can provide. That is because the machines are designed to give you upper AND lower body exercise, at a ratio that matches the natural ratio of upper to lower body muscle mass.
As with any exercise program, you should always talk to your doctor before you begin. Only your doctor can advise you as to the best exercise regime to meet your own personal needs.
But if you are healthy enough for exercise and concerned about joint pain or damage, elliptical machines are probably the least likely exercise equipment to cause injury during your workout. Many doctors can even suggest the best models to suit your own needs.