The muscle synergy hypothesis is an archetype of the notion of Dimensionality Reduction (DR) occurring in the central nervous system due to modular organisation. Towards validating this hypothesis, it is however important to understand if muscle synergies can reduce the state-space dimensionality while suitably achieving task control. In this paper we present a scheme for investigating this reduction, utilising the temporal muscle synergy formulation. Our approach is based on the observation that constraining the control input to a weighted combination of temporal muscle synergies instead constrains the dynamic behaviour of a system in trajectory-specific manner. We compute this constrained reformulation of system dynamics and then use the method of system balancing for quantifying the DR; we term this approach as Trajectory Specific Dimensionality Analysis (TSDA). We then use this method to investigate the consequence of minimisation of this dimensionality for a given task. These methods are tested in simulation on a linear (tethered mass) and a nonlinear (compliant kinematic chain) system; dimensionality of various reaching trajectories is compared when using idealised temporal synergies. We show that as a consequence of this Minimum Dimensional Control (MDC) model, smooth straight-line Cartesian trajectories with bell-shaped velocity profiles are obtained as the solution to reaching tasks in both of the test systems. We also investigate the effect on dimensionality due to adding via-points to a trajectory. The results indicate that a synergy basis and trajectory-specific DR of motor behaviours results from usage of muscle synergy control. The implications of these results for the synergy hypothesis, optimal motor control, developmental skill acquisition and robotics are then discussed
