The invention relates to a connecting mechanism adaptive to free movement of a self-deformation member space, comprising a free member with self-deformation characteristics, a supporting platform, and three combined auxiliary branched chains and three mobile auxiliary branched chains which are alternately fixed on the free member. The supporting platform is arranged around the middle part of the periphery of the free member, and clearance is arranged between the supporting platform and the free member; the combined auxiliary branched chains respectively comprise two pairs of spherical hinges and a member connection piece; each pair of the spherical hinges can respectively form a spherical pair in a fit and rotating manner; the two spherical pairs are connected in series by the member connection piece and symmetrically distributed on the upper side and the lower side of the supporting platform, and the upper end part and the lower end part of the member connection piece are fixedly connected on the free member; and one end of each of the mobile auxiliary branched chains is fixedly connected on the free member, and the other end thereof is arranged on the supporting platform in a slidable manner to form a mobile pair. The connecting mechanism can achieve local small displacement and overturning at 360 degrees of the free member and can adapt to heavy-duty working conditions.