A Shock Mitigation of Pedestrian-Vehicle Impact Using Active Hood Lift System: Deploying Time Investigation

This paper investigates the deploying time (or response time) of an active hood lift system (AHLS) of a passenger vehicle activated by gunpowder actuator. In this work, this is accomplished by changing principal design parameters of the latch part mechanism of the hood system. After briefly introducing the working principle of the AHLS operated by the gunpowder actuator, the governing equations of the AHLS are formulated for each different deploying motion. Subsequently, using the governing equations, the response time for deploying the hold lift system is determined by changing several geometric distances such as the distance from the rotational center of the pop-up guide to the point of the latch in the axial and vertical directions. Then, a comparison is made of the total response time to completely deploy the hood lift system with the existing conventional AHLS and proposed AHLS. In addition, the workable driving speed of the proposed AHLS is compared with the conventional one by changing the powder volume of the actuator.


Introduction
Because of the increasing awareness of pedestrian safety and strengthening the related regulations, certain systems to reduce pedestrian injuries and prevent accidents have been greatly developing in vehicle systems [1][2][3][4].One of advanced systems to achieve this goal is to use an active hood lift system (AHLS) which lifts the hood of an automobile when the vehicle collides with the pedestrian [5][6][7][8][9].The main role of the AHLS is to absorb the shock that would normally be transmitted to the pedestrian, like an airbag for the driver.In other words, this system makes the available deformation space of the hood at internal room by raising the hood for protecting pedestrian from colliding with hard structures like the engine.In particular, this system greatly reduces an injury of the pedestrian's head, which causes the majority of fatalities [10,11].It has been reported that when the AHLS is applied in a head impact test, the head impact performance criterion (HPC), which represents the injury value of the head, can be reduced by a maximum of 90% [5,12].Furthermore, it has been mathematically assessed that the pedestrian lives of maximal 80% could be saved by the AHLS [13].In the past, the conventional AHLS only raised the hinge part located at the rear of the hood.However, recently, the latch part located at the front of the hood has also been considered to be important to achieve better performance, especially for the child pedestrian that collides with front area of hood.In the operation of the AHLS, the most important factor to save the pedestrian is the developing time (response time) after the first collision.Because a sufficient operational speed has not yet been achieved, the operation cannot be completed before colliding with the pedestrian's head.Thus, a slow response time may cause a terrible impulse to the pedestrian due to the kinetic energy of the hood.
Recently, a new AHLS activated by gunpowder was introduced, and it was verified that it could be operated at a vehicle speed of 60 km/h.In contrast, the conventional AHLS normally operates at less than 40 km/h.When the driving speed is 40 km/h, the time from the first collision to contact with the hood is about 60 ms [14].It is generally known that the sensing time and processing time of an electronic control unit (ECU) are 30 ms, and the response time of the hood system is 30 ms [15].But, when the driving speed is 60 km/h, the time to contact with the hood is 40 ms, and thus the necessary response time of the AHLS should be sharply decreased to 10 ms.However, in this system, the extremely careful treatment should be given to the increase of workable driving velocity of the system when the increase of critical damage is considered.In the worst case, the collision could occur before the operation because of the potential variation in the explosive of the gunpowder actuator, and hence the pedestrian may take damage that surpasses the impact of vehicle in 60 km/h.This is caused by the kinematic energy of the hood system.Therefore, the relationship between several workable driving velocities and the deploying time of the active hood system needs to be investigated.In particular, careful treatment should be given to the design of the latch part of the AHLS which is crucial for the safety of a child pedestrian.This is because the latch part located in the front part of the hood directly affects the response time of the AHLS which is a significant factor in mitigating serious injury to a child from the collision.Also, as mentioned earlier, it is very important to study the design parameters of the latch part to reduce the response time in relation to fatal pedestrian accidents because the AHLS can protect pedestrians at a broader range of vehicle speeds by reducing the response time.Today, there is a sharp increase in the number of fatal accidents when the driving speed increases [16,17].In addition, it should be noted that lifting the hood higher through a shorter time can provide some benefits by absorbing the impact energy of the pedestrian.In other words, a pedestrian is protected more safely from the hard structure beneath the hood when the hood is lifted higher through the response time reduction.Despite the significance of reducing the response time of the AHLS, the research reported on this issue is considerably rare.
Consequently, the main technical contributions of this work are summarized as follows: (1) the investigation of geometrical effects of the latch part mechanism in the AHLS on the deploying time in a collision with a child pedestrian, (2) the investigation of the relationship between several workable velocities which include worse circumstance than conventional regulation in which the child pedestrian should be saved under the vehicle speed of 40 km/h, (3) the determination of principal geometrical parameters to significantly reduce the deploying time, and (4) the demonstration of the faster deploying time of the proposed method with the determined principal geometrical parameters than the conventional method.In order to achieve these goals, a mathematical model of the AHLS is firstly formulated for each deploying motion.In this formulation, the dominant design factors of the latch that are sensitive to the performance index are defined in the governing equations of motion.In the design process, the structural constraint conditions of the system, such as the limited space, are defined in detail.Because the response time of the system is an important factor for reducing a pedestrian's injuries, the kinematic structure of the AHLS is newly designed to decrease the response time under the imposed constraint conditions.A comparison between the proposed AHLS and the conventional one is performed in terms of the response time.It is shown that the newly designed AHLS gives much better performance than the conventional one showing faster response time at several gunpowder volumes.

Working Principle of AHLS
Figure 1 presents photographs showing the real operation of a passenger vehicle equipped with an AHLS.The vehicle's hood is raised immediately based on the sensor signal when it collides with an adult legform, as shown in Figure 1(b).The system raises both the front and rear of the hood to reduce the pedestrian impact using the AHLS installed at the latch and hinge of the hood.The latch part of the AHLS deployed by the gunpowder actuator consists of many elements named as bracket release, pop-up guide, emergency pawl, and pin striker as shown in Figure 2. It is seen that the vehicle hood can be raised by actuating the vertical motion of the latch part.When the pedestrian's leg collides with the bumper of the automobile, the actuator is exploded based on the sensor signal.The emergency pawl has a role of holding the system and preventing an unexpected release and the spring affects each element involved in maintaining the ordinary position.Figure 3 shows the operation sequence of the latch part, which is divided into four steps.The system operates sequentially from (A) to (E).These five points serve as the boundaries for the four steps, which are governed by different dynamic equations for the changed structure.Point (A) represents the initial structure that has the first contact between actuator and bracket release.At point (B), the pop-up guide meets the latch for the first time.At point (C), the pin striker which rotates with the pop-up guide meets the emergency pawl.At point (D), the resistance of the emergency pawl is released.Finally, the operation  is completed at point (E).In order to make it easier to understand the working principle, the operation sequence of a performance evaluation test of a conventional AHLS is shown in Figure 4.It is clearly seen from the photograph that the height of the hood increases as time goes on.The white triangle indicates lifted height of the latch part while the black triangle indicates the original location.As shown in the figure, the latch part that is directly connected to the hood is lifted over the time.In this test, the system has a final height of 30 mm, and the operation is completed about 10 ms after the actuator operates.The actuator is operated by a micro gas generator (MGG) that quickly generates a large quantity of gas from the gunpowder.This system uses an MGG that produces a pressure of 35 MPa in a 10 cc volume when time passes 10 ms after the gunpowder is exploded.

Dynamic Equations
The governing equations of motion for the deployment of the AHLS are derived in order to determine the operating speed  1.The mass of the hood that is lifted at the total system is about 16 kg.However, the system raises both the front and rear of the hood installed at the latch and hinges of the hood.
Because of the distance from the center of mass of the hood to each place installed, the mass of the hood applied to the latch system is about 6.67 kg.
The actuator force that is transmitted to the bracket release is set at  1 in this work.The value of  1 depends on the deployed distance of the actuator and an internal volume change due to this deployed distance.As previously mentioned, the actuator force comes from an internal pressure change by the MGG. Figure 5(a) shows the pressure change of 35 MPa MGG in a 10 cc volume, and Figure 5(b) shows the internal pressure change of the actuator, in which the initial internal volume of the actuator (660 mm 3 ) is applied.On the other hand, Figure 6 shows the actuator force with no volume change, which is represented by multiplying a cross-sectional area of the actuator (38.5 mm 2 ) by its internal pressure change with a fixed initial volume.Consequently, the real actuator force  1 can be solved using the actuator force with no volume change and the volume change of the actuator over time.The volume change of the actuator is presented by multiplying its cross-sectional area and the deployed distance by the time that is represented by the entire distance  1 and  1 which is the rotated angle of the bracket release as shown in Figure 7. Thus, the real transmitted force and changed internal volume of the actuator are, respectively, defined as follows: Real Transmitted Force

=
Actuator Force × Initial Internal Volume of Actuator Changed Internal Volume of Actuator ,  Distance for moment transmitted to emergency pawl by friction force between pin striker and emergency pawl values of distances to calculate the moment of components, which change over time, are given as follows:

Changed Internal Volume of Actuator
Because bracket release and pop-up guide make a contact through the circle to circle after step All the variables used for dynamic equations derived to determine the response time and velocity at each step are presented in Table 3. Figure 8 shows a free body diagram for solving the moment using the force and friction force at step 1. Figure 8 Based on these free body diagrams, the dynamic equation of the bracket release at step 1 is derived using the sum of the moments, as given in (3).
Because the actuator is not initially in contact with the bracket release, the short deployed time of the actuator from the initial state to point (A) exists.So that is considered to apply  1 to derive the dynamic equation accurately and that time is 0.2 ms.And the initial spring torque of the bracket release is 1 Nm. Figure 8(c) presents a free body diagram showing the forces of the pop-up guide at step 1, and Figure 8(d) presents a free body diagram showing the friction force of the pop-up guide at step 1.Similarly, the dynamic equation for the pop-up guide at step 1 is derived as given in (4).And the initial spring torque of the pop-up guide is 1 Nm.Force transmitted by bracket release to pop-up guide  3 Force transmitted by pop-up guide to latch  5 Force transmitted by pop-up guide to emergency pawl In the above,   is the coefficient of rolling friction and   is the sliding friction coefficient.The solutions obtained at this stage indicate the finish time and final angle velocity of step 1, and hence they become the initial conditions of step 2.
Figure 9 shows a free body diagram for solving the moment at step 2. Figure 9 In the above,  1 is the finish time of step 1.  11 and  12 are final angles of bracket release and pop-up guide in step 1.
It should be noted that ( 8) is the dynamic equation of the bracket release.Equation ( 9) is the dynamic equation of the pop-up guide, and ( 10) is the dynamic equation of the latch.Equation (11) is the geometric relation between  1 and  2 at this step, and ( 12) is the geometric relation between  2 and  at step 2. Similar to steps 1 and 2, the dynamic equations for steps 3 and 4 are derived from the free body diagrams shown in Figures 10 and 11.The derived equations are given as follows.
Step 3. Consider  Step 4. Consider In the above,  2 is the finish time of step 2 and  3 is the finish time of step Figure 12 shows a flowchart that presents a specific method for solving the response time of the system using the derived dynamic equations.The final force, final angle velocity, and final position of the previous step become the initial conditions of the next step.The finish time of each step is defined as the time that the dynamic motion satisfies a particular condition of the step.The condition is set up as a function of  virtual or the lifted height of the hood, .Step 1 is completed when  virtual increases by 8 mm from point (A), and the operation reaches point (B) in Figure 3.That time is defined as the finish time of step 1,  1 .Step 2 is completed when  increases by 6 mm from point (B) and the operation reaches point (C).That time is defined as the finish time of  4), ( 5), (6), and ( 7) Division 2: (8), ( 9), ( 10), (11), and ( 12) Division 3: ( 13), ( 14), ( 15), ( 16), ( 17), (18), and ( 19) Division 4: (20), ( 21), ( 22), (23), and ( 24) x virtual is increased by 6 mm to point (B) Point (B): x is increased by 6 mm to point (C) Point (C): x is increased by 4 mm to point (D) Point (D): x is increased by 20 mm to point (E) Point (E): step 2,  2 .Step 3 is completed when  increases by 4 mm from point (C) and the operation reaches point (D).That time is defined as the finish time of step 3,  3 .Step 4 is completed when  increases by 20 mm from point (D) and the operation reaches point (E).That time is defined as the finish time of step 4,  4 .In addition, as mentioned earlier the deployed time of the actuator from the initial state to point (A) should be considered.That time is defined as  0 .Consequently, the sum of the finish times of the steps and initial deployed time of actuator becomes the total response time of the system.

Parametric Investigation
The main elements adjusted to reduce the response time denoted as  1 ,  2 ,  3 ,  4 ,  5 , and  6 are shown in Figure 13 and presented in Table 4.All of the distances to be adjusted for the new design are called "entire distances," and those distances are directly related to "equation distances."Therefore, the new distance can be found by changing the percentage of the entire distance and comparing the response time.The response time can be found using the flowchart shown in Figure 12, which is associated with the dynamic equations.In this work, the influence on the response time is investigated by changing the entire distance by −20%, −10%, +10%, and +20%, as given in Table 5.  1 ,  2 , and  4 have dominant influences, whereas the other distances have only slight influences on the response time.The response time decreases with increasing  1 and  4 and with decreasing  2 and  4 .Therefore, suitable  1 ,  2 , and  4 values should be suggested to reduce the response time.
In the practical application of the AHLS, several geometric constraint conditions exist.First, because of the internal distance limitation of the car, the maximum distances in  and  directions should be constrained.In this work, the maximum -direction distance of the internal space is considered to be 125 mm and that in the  direction is 120 mm.The entire distance should satisfy this spaceconstraint condition.In this case,  1 , which is the distance in the vertical direction, can be increased by 48% maximally and should not exceed 62 mm. 2 and  4 are distances in the horizontal direction, and their sum should not exceed 115.1 mm because of the space-constraint condition. 3 should not exceed 82.6 mm to satisfy the constraint.Specifically, the constraint conditions of  2 ,  3 , and  4 are caused by the existence of the emergency pawl and pin striker.It should be noted here that none of the numerical values used in this work are directly related to a certain car.Second, the height to be reached by the AHLS should be constrained using the geometric conditions of  2 ,  3 , and  4 .When the pop-up guide rotates until the operation is completed, the final height to be raised and distance  3 can have a geometric relation, as shown in Figure 14(a), which is expressed in mathematical terms by (25).When  3 is decreased to achieve better performance, the rotated angle  2 should be increased to maintain the fixed height.However, an increase in  2 may cause a delay in the response time.Thus, suitable  3 and  2 values should be found to satisfy the imposed geometric conditions.
In this work, the original height value is set at 30 mm, and the value of angle  is 0.35 rad, which is the initial angle of the pop-up guide between the -axis at point (B). 2 ,  4 , and Distance from rotational center of bracket release to end point at lift side of bracket release in horizontal direction  3 Distance from rotational center of pop-up guide to a point on latch part in the horizontal direction  4 Distance from rotational center of pop-up guide to contact point with bracket release in the horizontal direction  5 Distance from rotational center of pop-up guide to end point of pop-up guide  6 Distance from rotational center of emergency pawl to contact point with pop-up guide   2 also have a geometric relation, as shown in Figure 14(b), which simplifies the bracket release and pop-up guide at point (E), as shown in Figure 3.When the operation is finished, the final angle of the pop-up guide is represented by  2 value that is 20% smaller and  4 value that is 21% larger.Because of the thickness of the bracket release, its rotational center is located at a position that is lower than the initial position of the pop-up guide.When  4 is increased to achieve a suitable design,  2 also increases, because the changing rate of  4 is proportional to that of  2 to maintain a fixed value.However, increasing  2 may cause a delay in the operation.To reduce the response time, suitable  2 and  4 values should be found that satisfy the geometric conditions.The relation of  2 ,  4 , and  2 is mathematically expressed by (26), and the geometric condition of  2 ,  3 , and  4 is given by ( 27).It should be noted that the distance value of 13 mm is chosen for  in this work = 30 mm tan (0.35) + tan (tan −1 ((0.8 2 − 13 mm) /1.21 4 ) − 0.35) . (27)

Results and Discussions
A preferable structure for the AHLS to reduce the response time can be achieved by adjusting the dominant design factors.First, the suitable distances of   numerically through computer simulations that the proposed AHLS with the new design parameters provides a better performance than the conventional one in terms of the total response time, and the comparison results are presented in Table 8.The response time of the existing AHLS structure is 10.2 ms at 35 MPa MGG, which is very similar to the performance evaluation test result (10 ms) shown in Figure 4.It is seen from the table that the response time of the newly designed AHLS structure is 8.6 ms which is faster than the existing one.In addition, it is seen that when a 30 MPa MGG is used, the response time is reduced from 10.8 to 9.1 ms by the new design.In addition, when a 25 MPa MGG is used, the response time is reduced from 11.7 to 9.8 ms.As previously stated, the response time reduction is directly related to being able to operate at a high vehicle driving speed.Table 9 presents the workable driving speeds of vehicles when the response time of the AHLS is reduced based on this work.The workable driving speed is increased from 59.2 to 61.6 km/h when the new design is applied to the AHLS with an actuator that uses a 35 MPa MGG.It is also noticed from the table that the workable driving speed is increased from 58.3 to 60.8 km/h and from 57.2 to 59.8 km/h, with actuators that use a 25 MPa MGG and 15 MPa MGG, respectively.This increment of workable driving speed directly indicates the effectiveness of the proposed AHLS which can significantly reduce the collision injuries due to the fast deployment of the hood at higher vehicle speed.It is here remarked that the response time evaluated in this work indicates mechanical response time only after electronic processing.

Conclusion
In this work, a new geometrical design of an AHLS activated by a gunpowder actuator has been achieved to reduce the response time, which is directly related to the impact force to pedestrians during a collision.In order to accomplish this goal, the governing equations of motion at different deployment steps were derived from a free body diagram.Subsequently, a flowchart to calculate the total response time for the full deployment was made.After carefully investigating the influences of the design parameters on the response time, new values for the principal design parameters that could provide a faster response time were chosen with satisfying the geometric constraints.It has been demonstrated through a computer simulation that the proposed AHLS with the new design parameters provides a better performance than the conventional one in terms of the total response time.In addition, it has been observed that the response time can be shortened by changing the volume of gunpowder.This directly indicates that the response time of the AHLS can be shortened through both the actuator capacity (gunpowder volume) and geometric values.It is finally remarked that a solid analytical model integrated with optimization method such as a genetic algorithm will be developed as a second phase of this work in order to further reduce the response time of the AHLS to be deployed by the gunpowder actuator.

Figure 1 :
Figure 1: Operation photographs of vehicle equipped with AHLS: (a) before and (b) after actuation.
and response time.The geometric structure of the AHLS changes over time.Hence, the dynamic equation also changes over time.Therefore, the whole operation is divided into four steps with the boundary points shown in Figure 3.The operation that occurs from point (A) to point (B) in Figure 3 is step 1.The operation from point (B) to point (C) is step 2. The operation from point (C) to point (D) is step 3.The operation from point (D) to point (E) is the last step, step 4. The material properties used in this work are presented in Table Distance for moment transmitted to bracket release by reaction of pop-up guide  21 Distance for moment transmitted to pop-up guide by force of bracket release  22 Distance for moment transmitted to pop-up guide by reacted force of latch part  23 Distance for moment transmitted to pop-up guide by reaction of emergency pawl  24 Distance for moment transmitted to pop-up guide by reacted force of pin striker  31 Distance for moment transmitted to emergency pawl by force of pop-up guide  32 Distance for moment transmitted to emergency pawl by force of pin striker  1 Distance for moment transmitted to bracket release by friction force between bracket release and pop-up guide  2 Distance for moment transmitted to pop-up guide by friction force between bracket release and pop-up guide  3 Distance for moment transmitted to pop-up guide by friction force between pop-up guide and emergency paw  4 Distance for moment transmitted to pop-up guide by friction force between pop-up guide and pin striker  5 Distance for moment transmitted to emergency pawl by friction force between pop-up guide and emergency pawl  6
(a) presents a free body diagram showing the forces of the bracket release and Figure 8(b) presents a free body diagram showing the friction force of the bracket release.

Figure 8 (
Figure 8(e) presents a free body diagram showing the forces of the emergency pawl and Figure 8(f) presents a free body diagram showing the friction force of the emergency pawl at step 1.Then, the dynamic equation for the emergency pawl at step 1 is derived as given in(5).And its initial spring torque is 3 Nm.On the other hand,(6) is the geometrical relation between  1 and  2 and (7) is the geometric relation between  2 and  3 .As mentioned before, the distances  11 ,  12 ,  21 ,  22 ,  23 ,  24 ,  31 ,  32 ,  1 ,  2 ,  3 ,  4 ,  5 , and  6 are the distances used to calculate the moments transmitted by each force.Now, the unknown quantities of  1 ,  2 ,  3 ,  2 , and  5 can be solved using the following five dynamic equations at step 1: (a) presents a free body diagram showing the forces of the bracket release and Figure 10(b) presents a free body diagram showing the friction force of the bracket release at step 2. Figure 10(c) presents a free body diagram showing the forces of the pop-up guide and Figure 10(d) presents a free body diagram showing the friction force of the pop-up guide at step 2. Similar to step 1, the dynamic equations at step 2 are derived from the free body diagrams as follows:

Figure 8 :
Figure 8: Free body diagram for solving moment at step 1: (a) free body diagram showing forces of bracket release, (b) free body diagram showing friction force of bracket release, (c) free body diagram showing forces of pop-up guide, (d) free body diagram showing friction forces of pop-up guide, (e) free body diagram showing force of emergency pawl, and (f) free body diagram showing friction force of emergency pawl.

Figure 9 :
Figure 9: Free body diagram for solving moment at step 2: (a) free body diagram showing forces of bracket release, (b) free body diagram showing friction force of bracket release, (c) free body diagram showing forces of pop-up guide by force, and (d) free body diagram showing friction force of pop-up guide showing force of emergency pawl.

Figure 10 :
Figure 10: Free body diagram for solving moment at step 3: (a) free body diagram showing forces of bracket release, (b) free body diagram showing friction force of bracket release, (c) free body diagram showing forces of pop-up guide, (d) free body diagram showing friction forces of pop-up guide, (e) free body diagram showing force of emergency pawl, and (f) free body diagram showing friction force of emergency pawl.

Figure 11 :
Figure 11: Free body diagram for solving moment at step 4: (a) free body diagram showing force of bracket release, (b) free body diagram showing friction force of bracket release, (c) free body diagram showing force of pop-up guide by force, and (d) free body diagram showing friction force of pop-up guide.

Figure 12 :
Figure 12: Flowchart for solving response time.

Figure 13 :
Figure 13: Distances of elements to be adjusted to reduce response time.

R 3 Figure 14 :
Figure 14: Geometric relation of height and dominant distance.

2 :𝑅 4 :
Force transmitted by bracket release to pop-up guide (N)  3 : Force transmitted by pop-up guide to latch (N)  5 : Force transmitted by pop-up guide to emergency pawl (N)  6 : Force transmitted by pin striker to emergency pawl (N)  1 : Friction force between bracket release and pop-up guide (N)  2 : Friction force between pop-up guide and emergency pawl (N)  3 : Friction force between pin striker and emergency pawl (N)  1 : Inertia moment of bracket release (m 4 )  2 : Inertia moment of pop-up guide (m 4 )  3 : Inertia moment of emergency pawl (m 4 )  4 : Inertia moment of pin striker (m 4 )   : Inertia moment of pop-up guide and pin striker (m 4 )  1 : Spring coefficient of spring installed at bracket release (N/m)  2 : Spring coefficient of spring installed at pop-up guide (N/m)  3 : Spring coefficient of spring installed at emergency pawl (N/m)  1 : Distance from rotational center of bracket release to bottom of bracket release in vertical direction (mm)  2 : Distance from rotational center of bracket release to end point at lift side of bracket release in horizontal direction (mm)  3 : Distance from rotational center of pop-up guide to a point on latch part in the horizontal direction (mm) Distance from rotational center of pop-up guide to contact point with bracket release in the horizontal direction (mm)  5 : Distance from rotational center of pop-up guide to end point of pop-up guide (mm)  6 : Distance from rotational center of emergency pawl to contact point with pop-up guide (mm)  1 : Rotated angle of bracket release (rad)  2 : Rotated angle of pop-up guide (rad)  3 : Rotated angle of emergency pawl (rad)  2 : Rotated angle of pop-up guide until operation is completed from start (rad)   : Rolling friction coefficient   : Friction coefficient  0 : The deployed time of actuator from the initial state to point (A) (ms)  1 : Finish time of step 1 (ms)  2 : Finish time of step 2 (ms)  3 : Finish time of step 3 (ms)  4 : Finish time of step 4 (ms)  11 : Final angle of bracket release in step 1 (rad)  12 : Final angle of pop-up guide in step 1 (rad)  13 : Final angle of emergency pawl in step 1 (rad)  21 : Final angle of bracket release in step 2 (rad)  22 : Final angle of pop-up guide in step 2 (rad)  31 : Final angle of bracket release in step 3 (rad)  32 : Final angle of pop-up guide in step 3 (rad).

Table 2 :
Variables for equation distances.
11Distance for moment transmitted to bracket release by actuator force  12 2 after step 2.  2 has a fixed value, 24 mm. 11 can be presented through the sine value of the rotational angle of the vertical line on the contact surface of actuator and bracket release to express the change over time.And  11 is the distance from the center of arc to the rotational center of bracket release, and the value of  11 is 47 mm.Similarly, the distance of  12 can be presented through the cosine value of the rotational angle of the vertical line on the contact surface of bracket release and pop-up guide.And  12 is the distance from the center of arc that indicates contact line of bracket release and pop-up guide to rotational center of bracket release, and the value of  12 is 23 mm.As mentioned, because bracket release and pop-up guide make a different contact,  12 can be presented through the cosine value of the rotational angle of bracket release.The distance of  21 is decreased by 7 mm from the 32 mm, while  virtual is increased by 8 mm.Here,  virtual is the reduced distance from the surface of pop-up guide to latch in vertical direction by the rotation of popup guide in step 1.In the same way, the distance of  21 is decreased by 3 from 25, while  that is the lifted distance of latch is increased by 6 mm. 21 can be presented by  21 that is the distance from the center of arc that indicates contact line of pop-up guide to rotational center of pop-up guide.And the value of  21 is 25 mm. 22 can be presented by  22 that is the distance from the rotational center of pop-up guide to the latch in horizontal direction, and  24 can be presented by  24 that is the distance from the rotational center of popup guide to the end point of the pop-up guide.And the values of  22 and  24 are 53 and 81 mm.The distance of  31 is decreased by 11 from 19, while  virtual is increased by 8 mm, and  32 is decreased by 16 from 18, while  is increased by 6 mm.And  1 and  1 can be presented by  12 . 2 and 2, several distances are presented differently after step 2.  12 is presented by  12 until step 2 and  12 after step 2. And  21 is presented by  21 and  21 in step 1 and step 2, respectively, and  21 after step 2.  1 and  2 are presented by  1 and  2 until step 2 and  1and  5 can be presented by  21 and  24 , respectively.Here,   is the radius of arc which is the contact surface of bracket release between bracket release and pop-up guide, and the value of   is 21 mm.  is the radius of arc that is contact surface of pop-up guide between bracket release and pop-up guide, and the value of   is 10 mm.

Table 3 :
Variables used in dynamic equation.Rotated angle of bracket release  2 Rotated angle of pop-up guide  3 Rotated angle of emergency pawl  1 Force transmitted by actuator to bracket release  2

Table 4 :
Variables for entire distances.Distance from rotational center of bracket release to bottom of bracket release in vertical direction  2

Table 5 :
Response time due to change in entire distance.
2 ,  3 , and  4 are obtained based on the imposed geometric constraints.The changing rate of  3 can be found by changing  2 and  4 using (27), and this variation can be applied to the dynamic equation.2and4arechangedby −20%, −10%, +10%, and +20% to investigate the influences on distance  3 and the response time, and the results are presented in Table6.The results show that the response time decreases by decreasing  2 and increasing  4 .It is also shown that  3 increases by decreasing  2 and increasing  4 .Consequently, in order to achieve a better performance in terms of the response time,  3 should be increased maximally.When  3 increases maximally while satisfying the geometric condition,  3 can be increased by 57.6%.When  3 increases by 57.6%,  2 becomes 0.351 rad from (25).Then, the mathematical relation between  2 and  4 can be expressed by(26).Therefore, the changing rate of  2 and the response time can be obtained by changing  4 .The influences on the response time and  2 of changing  4 by −10%, +10%, +20%, +30%, +40%, and +50% are presented in Table7.It can be seen that the

Table 6 :
Changing rate of  3 and response time due to changes in  2 and  4 .

Table 7 :
Changing rate of  2 and response time due to change in  4 .responsetime is decreased by increasing  4 , regardless of  2 .Consequently,  4 should be increased maximally to reduce the response time while satisfying the geometric condition.It can be increased by 85.9%, and  2 can be increased by 5.1%, based on the geometric relation.As  1 increases, the response time decreases according to Table5.Thus, in order to obtain a better performance,  1 should be increased maximally.1 can be increased by 18% and still satisfy the geometric condition.The dominant factors for reducing the response time can be checked based on the results of the previously discussed parameter studies. 1 increases by 48%,  2 increases by 39.5%,  3 increases by 58.8%, and  4 increases by 190.2%.In other words,  1 increases from 42 to 62 mm,  2 increases from 37 to 51.6 mm,  3 increases from 52 to 82.6 mm, and  4 increases from 22 to 63.8 mm.So it has been demonstrated

Table 8 :
Comparison of response times of existing AHLS and newly designed AHLS with different actuator specifications.

Table 9 :
Workable driving speeds of existing AHLS and newly designed AHLS with different actuator specifications. 3 : Distance for moment transmitted to pop-up guide by friction force between pop-up guide and emergency pawl (mm)  4 : Distance for moment transmitted to pop-up guide by friction force between pop-up guide and pin striker (mm)  5 : Distance for moment transmitted to emergency pawl by friction force between pop-up guide and emergency pawl (mm)  6 : Distance for moment transmitted to emergency pawl by friction force between pin striker and emergency pawl (mm)  11 : Distance for moment transmitted to bracket release by actuator force (mm)  12 : Distance for moment transmitted to bracket release by reaction of pop-up guide (mm)  21 : Distance for moment transmitted to pop-up guide by force of bracket release (mm)  22 : Distance for moment transmitted to pop-up guide by reacted force of latch part (mm)  23 : Distance for moment transmitted to pop-up guide by reaction of emergency pawl (mm)  24 : Distance for moment transmitted to pop-up guide by reacted force of pin striker (mm)  31 : Distance for moment transmitted to emergency pawl by force of pop-up guide (mm)  32 : Distance for moment transmitted to emergency pawl by force of pin striker (mm)   : Radius of arc that is contact surface of bracket release between bracket release and pop-up guide (mm)   : Radius of arc that is contact surface of pop-up guide between bracket release and pop-up guide after step 2 (mm) : Lifted height of hood (mm)  1 : Force transmitted by actuator to bracket release (N)