Significance of Bhikkhus uncovering their right shoulder

Often in the suttas one finds Bhikkhus who approach the Buddha reverentially uncover their right shoulder as a mark of respect. What is the significance of this practice? Is it cultural or is there a deeper significance? One example from the Ratnakuta sutra > At that time, Venerable Mahāmaudgalyāyana then arose from his seat, bared his right shoulder, and bowed with his head at the Buddha’s feet. Elsewhere in the sutra, > Perceiving Sumati Bodhisattva’s extraordinary intention, good roots, and sovereign authority, each bhikṣu uncovered his upper robe. They gave an offering to the Tathāgata by developing a great vow, saying...