Constant-force mechanisms (CFMs) can produce an almost invariant output force over a limited range of input displacement. Without using additional sensor and force controller, adjustable CFMs can passively produce an adjustable constant output force to interact with the working environment. In the literature, one-dimensional CFMs have been developed for various applications. This paper presents the design of a novel CFM that can produce adjustable constant force in two dimensions. Because an adjustable constant force can be produced in each radial direction, the proposed adjustable CFM can be used in applications that require two-dimensional force regulation. In this paper, the design formulation and simulation results are presented and discussed. Equations to minimize the output force variation are given to optimally choose the design parameters. A prototype of the two-dimensional CFM is tested to demonstrate the effectiveness and accuracy of adjustable force regulation. This novel CFM is expected to be used in machines or robots to interact friendly with the environment.