Most of the human daily activities include acyclic multi-contact motions. Yet, generating such motions is challenging because of its high-dimensional and nonlinear solution space made by combinations of individual movements of body parts. In this paper, we present a novel keyframe-based framework to automatically generate multi-contact character motions. Our system consists of two components: key-pose planning and interpolation. Given initial and goal poses in which each contact can be repositioned at most one time during the transition, our key-pose planning step generates intermediate key-poses that represent contact changes, taking into account a set of principles for goal-directed movements. Next, the key-poses of each joint are independently interpolated to generate an acyclic multi-contact motion. We demonstrate that our framework can synthesize plausible interaction motions with a number of man-made objects, such as chairs and bicycles, without using any motion data. In addition, we show the scalability of our method by creating a long-term motion of climbing a ladder.