This paper proposes a new method for estimating skeletal muscle forces using a model derived from dimensional analysis. It incorporates electromyography signals and muscle force–length, force–velocity, and force–frequency relationships as inputs. The purpose of this model is to provide more accurate estimates of individualized muscle forces to better predict surrounding musculoskeletal tissue and joint contact loading. The derivation begins with dimensional analysis and a selection of critical parameters that define muscle force generation. The resulting constitutive equation gives way to a unique application of inverse-dynamics, one which avoids the issue of indeterminacy when reaction moments and ligament loading are minimized in a joint. The ankle joint is used as an example for developing the equations that culminate into a system of linear equations. A muscle force model capable of being calibrated and then used to predict joint contact and surrounding tissue loading is critical in advancing biomechanics research areas like injury prevention, performance optimization, and tissue engineering, among others. This model's foundation in dimensional analysis, along with its inclusion of electromyography signals, gives promise that it will be physiologically relevant and suitable for application-based studies. A following paper, Part II, will evaluate this premise in an experimental setting.