Elliptical machines are exercising or training machines that are used to imitate walking, jogging, running or climbing exercises. Different from treadmill machines, elliptical machine users never leave their feet away from the pedals, which reduces the pressures to the ankle, knee, and hip joints, and significantly lowers the impact injuries of users’ joints. The configurations of the elliptical motion commonly mimic the natural paths of the ankle, knee, and hip joints for walking, jogging or running, which further decreases the strains and stresses on users’ joints. In addition to low joint impact, another feature of elliptical machines is their integrated leg and arm movements that provide the dual lower and upper body exercises. Users of elliptical machines not only exercise their legs, but also push and pull the handlebars to strengthen their arms. Unlike treadmills, ellipticals are self-powered by user-generated motion and have no need for motor and belt conveyance. The closed trajectories of elliptical machines are generated through their linkages. The shapes and sizes of the closed trajectories depend on the linkage dimensions. The trajectory of an elliptical machine needs to meet the requirements for different exercises, and various short and tall people with a wide range of arm or leg sizes. If an elliptical machine has fixed linkage dimensions, its elliptical trajectory has only one shape and size, which does not provide flexibility. In order for an elliptical machine to have flexibility, its linkage has to be adjustable. Adjustable linkages are more difficult to design than linkages without adjustability. This research is motived by surmounting the challenges facing elliptical machines. Different types of elliptical machines (rear, front, and central drives) without and with adjustability are analyzed. Their elliptical output motions are simulated. The research results will provide useful guidelines for developing and promoting elliptical machines.