Path coverage attracts many interests in some scenarios, such as object tracing in sensor networks. However, the problem of how to conserve the constrained energy of sensors is rarely considered in existing research. This paper studies two problems in the energy conservation of sensor networks that have not been addressed before. The first problem is called the least movement of nodes on path coverage. It first proves the problem as NP-hard, and then uses curve disjunction to separate each path into some discrete points, and ultimately moves nodes to new positions under some heuristic regulations. The utilized curve disjunction technique makes the proposed mechanism unrestricted by the linear path. The second problem is called the largest lifetime on path coverage. It first separates all nodes into independent partitions by utilizing the method of largest weighted bipartite matching, and then schedules these partitions to cover all paths in the network by turns. We eventually analyze the energy cost of the two proposed mechanisms, and evaluate the effects of some parameters on performance through extensive experiments, respectively.