Tensegrity structures are defined as unique mechanisms consisting of strut members, elements in a compressive state, and tie members, elements in a tensile state, arranged in an orientation in which the device is in a stable state of self-equilibrium. The process of arranging these elements in geometrically symmetric and asymmetric orientations while simultaneously satisfying several geometric and force constraints for tensegrity mechanisms is known as form-finding. This study begins with an analysis the two main classifications of tensegrity form-finding, form-controlled and force-controlled, along with their corresponding advantages and disadvantages. A tensegrity mechanism with four struts, known as a T-4 tensegrity mechanism, is then analyzed with respect to two new methods that address the disadvantages of several of the form-controlled and force-controlled processes. Computer aided design simulation and a forward position analysis algorithm are used in conjunction with non-linear constrained optimization to create a mathematical model of the T-4 tensegrity mechanism. Numerical examples of the two newly proposed form-finding methods are given not only to illustrate the advantages these processes have over current methods, but also to show how these methods can be used to aid users in creating accurate and stable tensegrity and tensegrity-based mechanisms.