Disclosure of Invention
In view of this, the present application provides a system and a method for testing a parking response time, so that the parking response time can be tested with fewer devices, and the testing method is simpler, has a relatively smaller testing error, and consumes relatively less time.
The first aspect of the application provides a parking response time testing system, which is connected with a tested vehicle and used for measuring the parking response time of the tested vehicle;
the test system comprises a mobile test component, a trigger component and a signal receiver;
when the mobile testing component passes through an alarm point of the tested vehicle, the triggering component can send out a first electric signal;
the signal receiver is at least provided with two input channels, wherein the two input channels comprise a first input channel and a second input channel, the trigger component is connected with the oscilloscope through the first input channel, and the sound output component of the vehicle to be tested is connected with the oscilloscope through the second input channel; the signal receiver is used for receiving the first electric signal and a second electric signal sent by the sound output component, and determining parking reaction time according to the first electric signal and the second electric signal.
Optionally, the signal receiver is an oscilloscope.
Optionally, the triggering component is a motor vehicle coil detector or a touch switch.
Optionally, the mobile test component comprises a mobile body and a test rod, and the test rod is mounted on the mobile body.
Optionally, the moving body includes a rolling body or a sliding body.
A second aspect of the present application provides a method for testing a parking response time, which is applied to a parking response time testing system, the testing system including a mobile testing component, a triggering component, and a signal receiver, the method including:
acquiring a first electrical signal and a second electrical signal; the first electric signal is sent by the trigger component when the mobile testing component passes through an alarm point of the tested vehicle, and the second electric signal is sent by a sound output component of the tested vehicle when the sound output component sends an alarm sound;
and determining parking reaction time according to the first electric signal and the second electric signal.
Optionally, if the signal receiver is an oscilloscope, the determining the parking reaction time according to the first electrical signal and the second electrical signal includes:
and determining parking reaction time according to the waveform of the first electric signal and the waveform of the second electric signal.
Optionally, the determining a parking reaction time according to the waveform of the first electrical signal and the waveform of the second electrical signal includes:
determining a time difference between a transition point of the waveform of the first electrical signal and a transition point of the waveform of the second electrical signal according to the waveform of the first electrical signal and the waveform of the second electrical signal;
and determining the parking reaction time according to the time difference.
Optionally, the method further includes:
and obtaining the multiple parking reaction time, and taking the average value of the multiple parking reaction time as the parking reaction time.
Optionally, the alarm point is determined by the following method:
controlling the mobile test component to move towards a detection area of a parking assist system of the tested vehicle;
when the tested vehicle gives out an alarm sound, marking the position of the mobile testing component on the ground;
and averaging the positions marked for multiple times, and determining the averaged positions as alarm points.
According to the technical scheme, the embodiment of the application has the following advantages:
in the embodiment of the application, the first electric signal which is triggered by the mobile testing part passing through the alarm point of the tested vehicle and is sent out by the signal receiver and the second electric signal which is sent out by the sound output part of the tested vehicle when the sound output part of the tested vehicle sends out the alarm sound are obtained by the signal receiver, the propagation delay is greatly reduced due to the fact that the electric signal is adopted to replace the sound signal, the signal receiver is adopted to replace a camera and a microphone to measure the parking reaction time, the error of equipment is greatly reduced, and the reaction time of millisecond (ms) unit required in the ISO related standard can be measured very accurately. In addition, in the testing process, special equipment such as a camera/a microphone and the like is not needed, the testing result can be synchronously given in the testing process, and special audio and video processing software is not needed to be adopted at a Personal Computer (PC) end for analysis, so that the testing specialty is reduced, the testing equipment cost is reduced, and the testing time is shortened.
Detailed Description
In order to make the technical solutions of the present application better understood, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
The terms "first," "second," "third," "fourth," and the like in the description and in the claims of the present application and in the drawings described above, if any, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the application described herein are, for example, capable of operation in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
The parking response time testing system is used for solving the technical problems that a parking response time testing method in the prior art is multiple in testing equipment types, complex in testing method, large in testing error and long in time consumption. The test system is connected with a tested vehicle and used for measuring the parking reaction time of the tested vehicle. The test system comprises a mobile test component, a trigger component and a signal receiver; when the mobile testing component passes through an alarm point of the tested vehicle, the triggering component can be triggered to send out a first electric signal; when the sound output component of the tested vehicle gives out the alarm sound, the second electric signal sent by the sound output component can be acquired; the signal receiver is provided with at least two input channels, wherein the two input channels comprise a first input channel and a second input channel, the first input channel of the signal receiver is connected with the trigger component, the second input channel of the signal receiver is connected with the sound output component of the tested vehicle, and therefore the signal receiver can determine the parking reaction time of the tested vehicle according to the first electric signal and the second electric signal.
Because the electric signal is adopted to replace the sound signal, the propagation delay is greatly reduced, and the signal receiver is adopted to replace a camera and a microphone to measure the parking response time, the error of the device is greatly reduced, and the response time of an ms-grade unit required by the ISO relevant standard can be accurately measured. In addition, in the test process, special equipment such as a camera/a microphone is not needed, the test result can be synchronously given in the test process, special audio and video processing software is not needed to be adopted at the PC terminal for analysis, the test specialty is reduced, the cost of test equipment and the cost of test time are reduced, and the test efficiency is greatly improved.
In order to facilitate understanding of the technical solution of the present application, a parking response time testing system provided in the present application will be described below with reference to the accompanying drawings.
Fig. 1 is a schematic structural diagram of a parking response time testing system according to an embodiment of the present application. The test system 100 is connected to the vehicle 200 to be tested, and is used for measuring the parking response time of the vehicle 200 to be tested. The test system 100 includes a mobile test unit 110, a trigger unit 120, and a signal receiver 130.
When the mobile testing component 110 passes through the alarm point of the tested vehicle 200, the triggering component 120 can send out a first electric signal;
the signal receiver 130 has at least two input channels, including a first input channel and a second input channel, the triggering component 120 is connected with the signal receiver 130 through the first input channel, and the sound output component 210 of the vehicle under test 200 is connected with the signal receiver through the second input channel;
the signal receiver 130 is configured to receive the first electrical signal and a second electrical signal emitted by the sound output component, and determine a parking reaction time according to the first electrical signal and the second electrical signal;
the second electrical signal is generated by triggering the sound output part 210 when the parking assist system 220 of the vehicle 200 detects an obstacle.
In the above embodiment, the alarm point refers to a position where an obstacle enters the detection range of the parking assist system 220 of the vehicle 200 under test to trigger an alarm. In this embodiment, the mobile testing component 110 may be used to simulate an obstacle entering the detection area of the parking assist system 220 of the vehicle 200 to be tested to trigger an alarm, and an alarm point may be determined according to the position of the mobile testing component 110 when the alarm is given.
In one possible implementation, the mobile test component 110 may be controlled to move to the detection area of the parking assistance system 220 of the vehicle under test 200, and when the vehicle under test 220 makes an alarm sound, the position of the mobile test component 110 on the ground is marked, and an alarm point may be determined according to the position. As a possible implementation, the position may be directly determined as the alarm point, or the above method steps may be performed multiple times, where the position of the mobile test component 110 on the ground is marked multiple times, the marked positions are averaged multiple times, and the averaged position is determined as the alarm point.
It should be noted that, the parking assist system 220 of the vehicle generally detects an obstacle by using ultrasonic waves, and the wave emitting direction of the ultrasonic sensor at the middle position is toward the rear of the vehicle, and since the ultrasonic energy has a characteristic of being attenuated with an increase in distance, and is influenced by environmental factors such as temperature, wind speed, humidity, pressure, and the like, the distance measurement stability is influenced to a certain extent. If an obstacle or a test object is close to the vehicle in a direction perpendicular to the direction of the tail of the vehicle, namely, is close to the vehicle in a direction parallel to the wave-sending direction, a test result distortion caused by a distance measurement stability error may be generated, a more accurate alarm point is difficult to obtain, and an error is brought to the test of the parking response time.
Based on this, it is possible to control the mobile test member 110 to approach the vehicle 200 under test from the direction perpendicular to the wave generation direction, and to determine the alarm point according to the position of the mobile test member 110 when the alarm sound is emitted. For convenience of description, the longitudinal direction of the vehicle, i.e., the front-rear direction of the vehicle, is defined as the x-axis, the lateral direction of the vehicle, i.e., the left-right direction, is defined as the y-axis, and the height direction is defined as the z-axis. Since the wave-emitting direction is parallel to the x-axis, a direction perpendicular to the wave-emitting direction, i.e., the x-axis, may be any direction parallel to the YZ plane. Figure 2 shows a schematic view of a mobile test part in proximity to a vehicle under test. As shown in fig. 2, the mobile testing part 110 can approach the vehicle 200 to be tested in any direction on the YZ plane, for example, it can approach the vehicle 200 to be tested in a direction parallel to the rear direction of the vehicle, approach the vehicle 200 to be tested in an inclined direction on the YZ plane, or approach the vehicle 200 to be tested in a direction parallel to the height direction of the vehicle. Compared with the traditional test method which can only determine the alarm point through the height direction, the test method provided by the application can determine the alarm point from any direction perpendicular to the wave-sending direction, so that the determination of the alarm point is easier.
Further, an area corresponding to 80% of the maximum probing distance at the rear of the vehicle 200 under test may be used as a movement area of the moving test part, and the moving test part may be controlled to move toward the probing area in the YZ plane. Figure 3 shows a schematic diagram of controlling the movement of a moving test part. As shown in fig. 3, the detection area of the vehicle under test may be determined first, and then the maximum detection distance of the vehicle under test may be determined, so that an area of 80% of the maximum detection distance may be determined, and the area may be determined as the movement area of the movable test member. As a specific example of the present application, the mobile test part 110 may be controlled to move slowly in a direction parallel to the rear of the vehicle in the moving area, and an alarm point may be determined according to the alarm sound. It should be noted that 80% is only an empirical value for determining the moving area in the embodiment of the present application, and in other possible implementations, other proportional values may be used to determine the moving area.
After the alarm point is determined, the triggering component 120 may be mounted on the ground of the alarm point such that moving the testing component 110 past the ground of the alarm point causes the triggering component 120 to be triggered to emit the first electrical signal. As a possible implementation, the triggering device 120 may be a coil detector of a motor vehicle or a touch switch. It should be noted that the coil detector or the touch switch of the motor vehicle described in the foregoing embodiment does not limit the technical solution of the present application, and in other possible implementation manners of the embodiment of the present application, other triggerable components may also be used to implement the function of triggering the first electrical signal, which is not limited in this application.
In the above embodiment, in order to realize the measurement of the parking response time, it is necessary to simulate the movement of an obstacle to an alarm point using the movement test part 110. It can be seen that the mobile test component 110 is a mobile component for testing the parking response time. The movable testing component 110 may be an integral component integrating the moving and testing functions, or may be a component assembled by a movable component and a testing component. In one possible implementation, the mobile testing component 110 may include a mobile body and a test stick mounted on the mobile body. The movable body refers to a movable object, and includes a rolling body or a sliding body. As a specific example of the present application, the moving body may be a moving cart. The test rod may be a standard test rod as specified in ISO or related industry standards, for example the test rod may be a Polyvinyl chloride (PVC) tube having a diameter of 75 mm. Compared with an integral component integrating the moving and testing functions, the moving testing component consisting of the moving trolley and the testing rod can be conveniently disassembled and assembled, and is easy to store and manage.
In this embodiment, when the mobile testing component 110 passes through an alarm point, the triggering component 120 is triggered to generate a first electrical signal, and the alarm point belongs to a detection region of the vehicle under test, the parking assistance system 220 of the vehicle under test 200 can detect the mobile testing component 110, and then the sound output component 210 of the vehicle under test 200 generates an alarm sound. The sound output part 210 of the vehicle under test may be a speaker. It will be appreciated that the sound output component typically converts an electrical signal to a sound signal for output, and for this purpose the electrical signal may be retrieved from the sound output component and may be used as the second electrical signal.
The time of the first electric signal jumping is equivalent to the time of the appearance of the obstacle, the time of the second electric signal jumping is equivalent to the time of providing alarm information for a driver, and therefore the time difference of the first electric signal jumping and the second electric signal jumping is equivalent to parking reaction time. The signal receiver 130 may receive the first electrical signal and the second electrical signal and determine a parking response time based on the first electrical signal and the second electrical signal.
In one possible implementation, the signal receiver 130 may be an oscilloscope. An oscilloscope is an electronic measuring instrument that converts electrical signals that are difficult to see by the naked eye into a visualized image. The oscilloscope is provided with a plurality of input channels, the first electric signal and the second electric signal are respectively input into different input channels, and the first electric signal and the second electric signal can be simultaneously displayed. The oscilloscope can be used for observing various waveform curves of which the signal amplitudes change along with time, so that the oscilloscope can be used for testing voltage, current, frequency, phase difference, amplitude modulation and the like, the jump points of the respective waveforms can be determined according to the waveforms of the first electric signal and the second electric signal, and the parking reaction time can be determined based on the time difference of the jump points of the first electric signal and the second electric signal.
Therefore, the embodiment of the application provides a parking response time testing system, which comprises a mobile testing part, a triggering part and a signal receiver, wherein a first electric signal which is triggered by the mobile testing part when the mobile testing part passes through an alarm point of a tested vehicle and is emitted by the triggering part and a second electric signal which is emitted by a sound output part of the tested vehicle when an alarm sound is emitted are obtained through the signal receiver. In addition, in the test process, special equipment such as a camera/a microphone is not needed, the test result can be synchronously given in the test process, and special audio and video processing software is not needed to be adopted at the PC end for analysis, so that the test specialty is reduced, the test equipment cost is reduced, and the test time is shortened.
In order to more clearly understand the technical solution of the present application, the embodiment of the present application further provides a specific example of a parking response time testing system.
Fig. 4 is a schematic structural diagram of a parking response time testing system according to an embodiment of the present application, and as shown in fig. 4, the parking response time testing system includes an oscilloscope 2, a moving trolley 3, a testing rod 4, and a touch switch 6; the test rod 4 is arranged on the movable trolley 3 and can move along with the movable trolley 3, and the movable trolley 3 can move in the moving area 7; the oscilloscope is provided with two input channels, wherein the first input channel is connected with the touch switch 6, and the second input channel is connected with the loudspeaker 1 of the tested vehicle.
The movement range 7 of the mobile carriage 3 can be determined from the detection range 5 of the parking assistance system of the vehicle under test. Specifically, after the detection region 5 is determined, the maximum detection distance may be determined, and the position of 80% of the maximum detection distance may be marked in the detection region. The movement area of the trolley 3 may include the marked position, so that when the test bar 4 is moved to the marked position or a nearby position, an alarm may be triggered.
After the alarm point is determined in the above-described manner, the touch switch 6 may be installed on the ground of the alarm point, and then the parking response time may be tested using the test system. Specifically, the mobile trolley 3 is controlled to slowly move in the moving area 7 along the direction parallel to the tail of the vehicle, when the mobile trolley 3 passes through an alarm point, the touch switch 6 is triggered to send out a first electric signal, the test rod 4 on the mobile trolley 3 is detected by the parking auxiliary system, and a loudspeaker of the vehicle to be tested sends out alarm sound, wherein the alarm sound signal is obtained by converting the electric signal, and the electric signal can be obtained as a second electric signal. Because the oscilloscope 2 is respectively connected with the touch switch 6 and the loudspeaker 1 of the vehicle to be tested, the oscilloscope can receive the first electric signal and the second electric signal, and further determine the parking reaction time according to the first electric signal and the second electric signal.
The time that the touch switch is triggered is adopted to replace the time that the obstacle enters the detection area, the time that the loudspeaker gives the alarm sound replaces the time that the alarm information is provided for the driver, the first electric signal sent by the fact that the touch switch is triggered and the second electric signal sent by the fact that the loudspeaker gives the alarm sound are obtained through the oscilloscope, and therefore the time difference between the time that the touch switch is triggered and the time that the loudspeaker gives the alarm sound is obtained, and therefore the parking reaction time is determined. Because the propagation delay of the electric signal is small, the signal receiver has high precision, and the equipment error is greatly reduced, the reaction time of the ms-grade unit can be accurately measured. In addition, the test system can be realized by only a small number of components, professional equipment such as a camera and a microphone is not needed, and special audio and video processing software is not needed for analysis, so that the test specialty is reduced, and the test cost is also saved.
Based on the parking response time testing system, the application also provides a parking response time testing method. Next, a specific implementation of a parking response time testing method provided in the embodiments of the present application will be described with reference to the drawings.
Fig. 5 is a method for testing a parking response time according to an embodiment of the present application, where the method is applied to a parking response time testing system according to the embodiment, where the parking response time testing system includes a mobile testing component, a triggering component, and a signal receiver, and as shown in fig. 5, the method includes:
s501: acquiring a first electrical signal and a second electrical signal; the first electric signal is sent by the trigger component when the mobile testing component passes through an alarm point of the tested vehicle, and the second electric signal is sent by a sound output component of the tested vehicle when the sound output component sends an alarm sound.
The alarm point is a position point where the mobile test component is located when the tested vehicle gives an alarm sound. The alarm point may be predetermined before the parking response time test is performed. In one possible implementation, the mobile test component may be controlled to move towards a detection area of a parking assistance system of the vehicle under test; when the tested vehicle gives out an alarm sound, marking the position of the mobile testing component on the ground; and determining an alarm point according to the position of the mark. In order to improve the accuracy of the alarm point, the alarm point can be marked for multiple times, the positions marked for multiple times are averaged, and the averaged position is determined as the alarm point.
After the alarm is determined, the mobile test part is controlled to slowly move in the direction perpendicular to the wave sending direction, for example, slowly move in the Y direction, when the mobile test part reaches the alarm point, the triggering part is triggered to send out a first electric signal, the mobile test part is detected by a parking assisting system of the tested vehicle, the tested vehicle sends out an alarm sound, and the sound output part of the tested vehicle can send out a second electric signal.
The signal receiver is connected with the triggering component and the sound output component of the tested vehicle respectively, so that the first electric signal and the second electric signal can be acquired.
S502: and determining parking reaction time according to the first electric signal and the second electric signal.
The time for the first electric signal to jump corresponds to the time for the obstacle to appear, and the time for the second electric signal to jump corresponds to the time for providing alarm information to the driver, so that the difference between the jumping times of the first electric signal and the second electric signal corresponds to the parking reaction time. Based on this, the response time of the parking assistance system, i.e. the parking response time, can be determined from the first electrical signal and the second electrical signal.
In some possible implementations of the present embodiment, the signal receiver may be an oscilloscope. When the signal receiver is an oscilloscope, the oscilloscope may receive the first electrical signal and the second electrical signal, and determine the parking reaction time according to a waveform of the first electrical signal and a waveform of the second electrical signal.
The determination of the parking response time according to the waveform of the first electrical signal and the waveform of the second electrical signal may be implemented in various ways. It can be understood that the waveform of the first electrical signal changes in amplitude after passing through the triggering component, that is, the waveform of the first electrical signal jumps, so that the time for jumping the waveform of the first electrical signal is equivalent to the time for triggering the triggering component when an obstacle appears, and similarly, the waveform of the second electrical signal changes when the sound output component sends an alarm sound, that is, the amplitude suddenly increases, that is, the waveform of the second electrical signal jumps when the sound output component sends the alarm sound, and the time for jumping the waveform of the second electrical signal is equivalent to the time for providing the alarm information to the driver. Based on this, in one possible implementation manner, the jumping point of the waveform of the first electric signal can be determined according to the waveform of the first electric signal, the jumping point of the waveform of the second electric signal can be determined according to the waveform of the second electric signal, and the parking reaction time can be determined according to the time difference between the jumping point of the first electric signal and the jumping point of the second electric signal. For example, the time difference between the transition point of the first electrical signal and the transition point of the second electrical signal is used as the parking response time.
In some cases, such as when the triggering component is triggered to cause a change in the phase of the first electrical signal, the phase difference between the first electrical signal and the second electrical signal may be determined according to the waveform of the first electrical signal and the waveform of the second electrical signal, and then the parking response time may be determined according to the phase difference. The parking response time is determined according to the phase difference, and is obtained according to the conversion relation between the phase difference and the time difference. For example, the phase difference between the first electrical signal and the second electrical signal is pi, the signal period is T, and each period generates a phase difference of 2 pi, so that the first electrical signal and the second electrical signal are actually separated by a half period, namely 0.5T, and thus the parking reaction time can be determined to be 0.5T.
In the above embodiments, the parking response time may be directly read from an oscilloscope. Since the waveform feeds back the change relation of the amplitude of the signal along with the time, the time difference between a certain position of the first electric signal and a corresponding position of the second electric signal can be directly read as the parking reaction time. For example, the time difference between the first peak and the second peak of the first electrical signal may be read as the parking response time, and the time difference between the first valley and the second valley of the second electrical signal may be read as the parking response time. When it needs to be explained, the position of the first electrical signal is not fixed, and may be a first peak, a first trough, or an nth peak, where N is a positive integer; in addition, the position of the first electrical signal is not limited to the peak or the trough, and the time difference between the first electrical signal and the second electrical signal can be read according to the time points of the waveform at other positions. By comparison, at the peak or trough position, the parking response time can be read more easily.
In some possible implementation manners of the embodiment, the multiple parking reaction time can be obtained, and the average value of the multiple parking reaction time is used as the parking reaction time, so that the accidental deviation in the single measurement process can be reduced, and the measurement accuracy of the parking reaction time is improved.
As can be seen from the above, the embodiment of the present application provides a specific implementation manner of a method for measuring a parking response time, a signal receiver is used to obtain a first electrical signal generated by a trigger component triggered when a mobile test component passes through an alarm point of a vehicle to be tested, and a second electrical signal generated by a sound output component of the vehicle to be tested when an alarm sound is generated, because an electrical signal is used to replace a sound signal, propagation delay is greatly reduced, and a signal receiver is used to replace a camera and a microphone to measure a parking response time, errors of equipment are greatly reduced, and a response time of an ms unit required in an ISO related standard can be very accurately measured. In addition, in the test process, special equipment such as a camera/a microphone is not needed, the test result can be synchronously given in the test process, and special audio and video processing software is not needed to be adopted at the PC end for analysis, so that the test specialty is reduced, the test equipment cost is reduced, and the test time is shortened.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the above-described systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
In the several embodiments provided in the present application, it should be understood that the disclosed system, apparatus and method may be implemented in other manners. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the units is only one logical division, and other divisions may be realized in practice, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
The above embodiments are only used for illustrating the technical solutions of the present application, and not for limiting the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions in the embodiments of the present application.
It should be understood that in the present application, "at least one" means one or more, "a plurality" means two or more. "and/or" for describing an association relationship of associated objects, indicating that there may be three relationships, e.g., "a and/or B" may indicate: only A, only B and both A and B are present, wherein A and B may be singular or plural. The character "/" generally indicates that the former and latter associated objects are in an "or" relationship. "at least one of the following" or similar expressions refer to any combination of these items, including any combination of single item(s) or plural items. For example, at least one (one) of a, b, or c, may represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", wherein a, b, c may be single or plural.