Theoretical analysis is convenient for analysis, t0 is the current time, A0 generation of the current time leader's technology, at the T1 level; B0 generation of the current time behind the technical point, at the T0 level. If they are developed as usual, by the time t1 and t2, the former reaches the points A1 and A2, while the latter reaches the points B1 and B2. The technical gap between the two is T2-T1, T3-T2; and will continue. If the laggard takes a leap behavior at t0 and establishes that it catches up or exceeds the leader at time t1 or t2, then the path spanning difficulty of exceeding or catching up with the leader at time t1 is ctgθ1=T3-T0t1-t0, ctgθ2 =T2-T0t1-t0, ctgθ1>ctgθ2, for the same reason, you can analyze the direct path difficulty of catching the leader at time t2; obviously, the smaller the θ angle, the greater the difficulty; the difficulty of crossing depends on the speed of the jump, the faster the speed, the difficulty The bigger. If the laggards want to implement technology leapfrogging, the spanning driving force P must be greater than or equal to the spanning resistance f to initiate the spanning and form the spanning speed VT. The direct path means that the initial time (t0) of the preparation technology span must be able to be achieved. The ability to catch up with or exceed the resources necessary for the leader's technological innovation capabilities. Technical Leaping Difficulty 212 If the spiral path analysis cannot meet the necessary conditions such as talents and funds for direct path crossing at the initial stage, it can form a technically spanned spiral support system under certain cooperative conditions by integrating relevant resources of itself and the organization. Technology crossover is implemented with a spiral path of strategic combinations. The radius of the spiral system is related to the number of other organizations (or individuals) that need to cooperate and the degree of cooperation. The more the number of cooperative organizations, the greater the degree of cooperation and the greater the r. In the precession system, the precession path is: x = rcos(ωt); The span is formed to form a velocity V along the direction of the spiral trajectory, the spanning velocity VT=Vsinα, and the precessional angular velocity ω=(Vcosα)/r. Thus, the precession path can be changed to: x=rcos(Vtcos(α/r), y =rsin(Vtcos(α/r),z=Vtsin(α). μ is generally small, and mg (sinα+μcosα) is smaller than mg, indicating that the driving force P required to achieve technical crossing is reduced under precession conditions. Maintaining a certain precession speed V, α can increase as the driving force increases, and the speed VT of the technology span is also accelerated. Under certain conditions of driving force, it is necessary to select the appropriate α to maintain the precession speed V, to initiate and realize the technical leap. Cross the path S=T/sinα. The required energy E = PS = mg (T + Tμctgα), Tμctgα > 0, so the precession span is more energy than the direct path span. That is, the technology of spiral propulsion spans the driving force required to sacrifice more energy in exchange for technology leap, thereby reducing the difficulty of technology leapfrogging and improving the efficiency of technology leapfrogging, enabling technology leapfrogging and achieving goals. From the point of view of the system's overall theory, the technical leap of spiral propulsion is composed of several subsystems (phase paths) that constitute the precession system as a whole (as shown), due to the parameters of the precession path V(t), r(t), α(t) is dynamic (Vi, ri, αi are constants in the ith phase), so there are either spiral paths or direct paths at different stages of the technology span. The spiraling crosses the path to show the dynamic precession and cross-over path. 3 Case analysis 311 Chinese photo-printing technology spans the leap of laser photo-distribution technology hosted by Wang Xuan, from the 1975 plan to the industrial application in 1987, after 12 years of hard work Relying on independent and cooperative technological innovation to achieve technological leapfrogging <8-12>. From the process of system development, after roughly six stages, it has emerged as a mutual transformation of the constraints of human resources and capital resources, and dominates the system. The way of development and solution is now the alternate advancement of autonomy and cooperation. The path that its technology spans is shown in Figure 4. The spiral path of Chinese laser photo-sequencing technology is shown. (1) Peking University relies on its own scientific research strength to achieve a breakthrough in principle. When China launched the "748 Project" project in 1975, Wang Xuan proposed to use the second generation and third generation photo-alignment technologies adopted by developed countries such as the United States, Britain and Japan, based on the existing theoretical knowledge and research accumulation. The fourth-generation laser photo-distribution technology program emerged and was supported by the “748 Project†project and funding. Peking University established a research group consisting of 7 people including Wang Xuan and started basic research. Under the cooperation of the Department of Physics and other units, the core technology of Chinese laser photo-distribution was invented, and the first digital precision photo-alignment system prototype was developed, which won one European patent and eight Chinese patents. (2) Joint development organization and prototype trial success. The prototype is still quite far from the actual application, and a series of technical improvements and improvements are needed. The development of the system requires the introduction of engineering and technical personnel. To this end, Peking University organizes relevant personnel to form a system technology research organization, and works closely with Xinhua News Agency, Wuxi Electronic Computer Factory, Weifang Computer Company and other units to develop application technology. (3) Industrialization technology development - achieving technological leapfrogging. Peking University and Weifang Computer Company worked closely together to develop the Huaguang I-type electronic publishing system in 1979; the Huaguang II-type publishing system was launched in 1983, and the Huaguang III-type machine was introduced in 1986, on December 2, 1987, Under the joint efforts of the cooperation units, the "Economic Daily" realized the computer laser photo-sequencing, completed the industrialization technology development, and realized the true technological leap. Subsequently, Peking University established Peking University Founder to further increase investment and comprehensively promote the industrial application of Chinese laser photo-distribution technology. The Chinese laser photo-distribution technology spans and adopts an autonomous-cooperative mode to promote the development of the system. If the initial conditions are not sufficient, the rapid advancement of technology and rapid advancement can be adopted, and the leap-forward path of various strategies can be used to implement the leap. Different paths can achieve independent innovation capability, and through the independent innovation to achieve the catch-up and even leapfrogging of the leader's technology, the important thing is the goal, management, control, and timely, realistic strategic choices. CNC Machine Parts，OEM CNC Machined Parts，OEM CNC Machined Parts 3D Printing Prototype Co., Ltd. , http://www.nsrapidprototype.com