This thesis presents modeling and control of novel tensegrity joint based on Twisted and Coiled Polymer Muscle (TCPM) that is biologically inspired by the human elbow. The tensegrity principle that is used to construct this joint has made it structurally compliance. Therefore, this joint can be categorized as a compliance actuator. The modeling is performed by constraining the joint movement to 2 Degree of Freedom (DoF). As a result, the joint kinematics and dynamics can be simplified and approximated as rigid body movement. To actuate the joint, the length of the TCPMs can be controlled individually by Joule heating. This joint can be seen as a MIMO system subject to multiple constraints. These constraints are imposed by the TCPM and used to prevent the joint from failure during actuation. Model Predictive Control (MPC) is designed to control the joint movement. This controller is suitable to handle a multivariable system subject to constraints. MPC controller based on linearized model and Hammerstein-Wiener model are designed and their performance on controlling the joint is compared. Finally, trajectory tracking simulation with various cases is provided to assess the controller performance.