Robotic peg-hole insertion operation, the most widely used assembly model, has been extensively investigated. The objective is to design strategies, or hardware, in order to enable a robot to achieve the assembly operation with: (1) higher accuracy than that obtainable directly from the resolution of the robot, (2) a cost lower than manual labour prices and, (3) an operation time in the range from 1.0 to 2.5 secs. There are many strategies provided through the use of specially designed hardware, for example, force sensors and robotic flexible wrists. However, it is difficult to achieve robotic peg-hole insertion with high accuracy, low cost and high speed. In previous work, strategies were designed to achieve the assembly operations without using force sensors or RCC (H. Qiao, B. H. Dalay, J. A. G. Knight, 1996, Robotic assembly operation strategy investigation without force sensors through the research on contact point location and range of peg movement. Proceedings of the IMechE, Journal of Engineering Manufacturing , Vol. 210, pp. 289-307). The strategy development in our work is based on the back-projection concept and the analysis of the allowable range of the peg system, which is constrained by the geometry of the hole system. The allowable range of the peg in the peg-hole system has been established, and features of this allowable range have been studied in detail. Compared with our previous strategies, this paper provides a strategy where the number of the required operational steps is reduced and the assembly process is simplified. The validity of this new method and the allowable initial range of the strategy are also studied. The key point in this paper are as follows: (a) establishing the general allowable range for the peghole system with symmetrical regular polyhedral objects, rather than for the round peg-hole system only, (b) studying the characteristics about this allowable range in more detail and finding out simplified strategies by their utilization, and finding out the allowable initial range for the peg-hole system in the new strategy. This strategy only includes three steps with the peg: (i) first rotated around an axis normal to its axis, (ii) then pushed towards the hole, (iii) then rotated back and inserted into the hole. This paper develops a particular strategy with the following characteristics: (1) it can perform the assembly operation fast, reliably and precisely, (2) there is no need to use force sensors or flexible wrists (3) the operation is simplified through the use of contact forces between the peg and the hole. There are three steps involved in the operation process. This method has been successfully applied to the cylindrical peg-hole insertion operation based on a 29.99 mm diameter peg and a hole with a diameter clearance of 0.02 mm. The operational time averages 1.5 sec. The strategy has been further verified through the simulation process. In addition, other issues about the strategy investigation, which may lead to new strategies, have been discussed.