We present a new method for multi-contact motion planning which efficiently encodes internal dynamics of the robot without needing to use full models. Our approach is based on a five-mass model which is formulated by Cartesian points instead of joint angles. We solve direct optimization problems which include distance constraints between these points, Newtonian equations and integration constraints. We consider a given rhythm of contact switches but leave the phase-timings and contact positions free inside the optimization to provide more flexibility. Due to simpler equations and sparser problem structures, we can achieve very short optimization times in the order of few hundred milliseconds, which make the method suitable for application of online model predictive control. Aside from contact position and time adjustment properties, we can include precise foothold regions and synthesize dynamic motions by taking internal dynamics and momentums into account.