FPC flat cable connector

Abstract

The utility model discloses an FPC flat cable connector, and belongs to the field of electric connectors. The connector comprises a shell, a terminal and a locking bar. The front end of the housing is provided with a flat cable jack. The terminal comprises an upper cross arm, a lower cross arm and a connecting arm; the locking bar is arranged at the rear part of the shell and can rotate up and down between a locking angle position and an unlocking angle position, an abutting arm is arranged on the locking bar, and when the locking bar rotates towards the locking angle position, the rear end of the upper cross arm is pushed to move upwards through the abutting arm, so that the front end of the upper cross arm moves downwards; the shell is provided with a limiting plate protruding backwards, the limiting plate is elastic, a limiting sliding groove and a limiting blocking table are arranged on the inner side of the limiting plate, connecting shafts are arranged at the two ends of the locking bar in the length direction, the connecting shafts are limited in the limiting sliding groove, and a guide groove is formed in the rear side of the limiting blocking table. The FPC flat cable connector is reasonable in structural design, the connecting shaft can be prevented from being broken when the locking strip is installed, the terminals are reliably positioned, the FPC flat cable can be effectively locked when the locking strip is located at the locking angle position, and the FPC flat cable connector has good practicability.

Description

Technical Field

[0001] The utility model belongs to the field of connector structure design, and particularly relates to an FPC flexible cable connector. Background Art

[0002] An FPC (Flexible Printed Circuit) flexible cable, also known as a flexible circuit board flexible cable, is a circuit board made of a flexible substrate, with characteristics such as bending, folding, and twisting, and is suitable for occasions with strict space requirements. The FPC flexible cable has the advantages of light weight, thin thickness, good flexibility, high temperature resistance, corrosion resistance, etc., and is widely used in electronic products, such as mobile phones, tablet computers, cameras, automobiles and other devices. Generally speaking, the FPC flexible cable plays an important role in electronic products, provides more possibilities for product design, and can meet the high requirements for circuit connection in different fields.

[0003] An FPC flexible cable connector is a device used to connect an FPC flexible cable to other electronic devices, also known as a flexible circuit board connector. Among FPC flexible cable connectors, there is a front-insertion and rear-lifting connector. By setting a locking bar at the rear of the connector and a cable socket at the front of the connector, the FPC flexible cable is inserted through the cable socket, and then the FPC flexible cable is locked by rotating the locking bar. In the existing front-insertion and rear-lifting connector, the locking bar cooperates with the shaft grooves on the housing through the rotating shafts at both ends. During assembly, the rotating shafts need to be forcibly pressed into the shaft grooves to form a limiting connection. This assembly method is likely to cause damage (fracture) to the rotating shafts during installation, thereby affecting the service life of the FPC flexible cable connector. Summary of the Utility Model

[0004] The utility model aims to provide an FPC flexible cable connector to solve the above problems in the background art.

[0005] To achieve the above purpose, the utility model adopts the following technical solutions:

[0006] The utility model provides an FPC flexible cable connector, which comprises a housing, terminals and a locking bar; a flexible cable socket is arranged at the front end of the housing; terminal positioning holes are arranged on the housing, the terminal positioning holes are communicated with the flexible cable socket, and the terminals are inserted into the terminal positioning holes; the terminals comprise upper cross arms, lower cross arms and connecting arms, and the upper and lower ends of the connecting arms are integrally connected with the middle parts of the upper cross arms and the lower cross arms respectively; the locking bar is installed at the rear part of the housing and can rotate up and down between a locking angle position and an unlocking angle position, a resisting arm is arranged on the locking bar, and when the locking bar rotates towards the locking angle position, the rear end of the upper cross arm is pushed upwards by the resisting arm so that the front end of the upper cross arm moves downwards; limiting plates protruding rearwards are arranged at the rear parts of both ends in the length direction of the housing, the limiting plates are elastic, a limiting chute extending in the front-rear direction and a limiting stop platform at the rear side of the limiting chute are arranged on the inner side of the limiting plates, connecting shafts are arranged at both ends in the length direction of the locking bar, the connecting shafts are limited in the limiting chute, a guide groove for guiding the connecting shafts to pass through is arranged at the rear side of the limiting stop platform, and a slope surface is formed at the front part of the guide groove close to the limiting stop platform.

[0007] In some embodiments, clamping blocks are arranged at both ends of the locking bar, a first clamping groove is arranged on the inner side wall of the limiting plate, when the locking bar is in the locking angle position, the clamping blocks are clamped with the first clamping groove, when the locking bar is in the unlocking angle position, the clamping blocks are located above the limiting plate and are suitable for forming a resisting interference with the upper edge of the limiting plate to prevent the locking bar from rotating towards the locking angle position, and the guide groove and the first clamping groove have the same structure.

[0008] In some embodiments, a supporting shaft part arranged along the length direction of the locking bar is arranged at the bottom of the locking bar, an arc-shaped groove part with an upward opening is formed at the upper part of the rear end of the lower cross arm, the supporting shaft part is embedded in the arc-shaped groove part, and the contact surfaces of the supporting shaft part and the arc-shaped groove part are arc surfaces matching with each other.

[0009] In some embodiments, a front stop block and a rear stop block are respectively and upwards protruded at the front and rear sides of the arc-shaped groove part at the upper part of the rear end of the lower cross arm, and the height of the rear stop block is lower than that of the front stop block.

[0010] In some embodiments, a receiving groove is formed at the front-facing side of the locking bar in the locking angle position, side baffles are formed at both ends of the receiving groove, a convex edge extends rearwards from the upper side wall of the rear end of the housing and avoidance notches are formed at both ends of the convex edge, when the locking bar is in the locking angle position, the convex edge is suitable for extending into the receiving groove, and the side baffles are correspondingly located in the avoidance notches.

[0011] In some embodiments, a power connection arm and a fixing arm extending forward are formed at the front end of the lower cross arm. A bayonet is formed between the fixing arm and the power connection arm. A positioning block and a fixing jack located below the positioning block are provided at the bottom of the front end of the terminal positioning hole. The bayonet is inserted into the positioning block, and the fixing arm is tightly inserted and fixed in the fixing jack. A clamping protrusion formed by extending backward and obliquely is provided at the bottom of the power connection arm, and a second card slot cooperating with the clamping protrusion is provided at the upper part of the positioning block.

[0012] In some embodiments, an inclined angle is provided at the upper part of the rear side of the positioning block.

[0013] In some embodiments, a first antenna is provided at the lower part of the front end of the upper cross arm, and a second antenna is formed at the upper part of the power connection arm. The first antenna and the second antenna are in an inverted hook-shaped structure and have a pointed angle extending into the wire arranging socket.

[0014] In some embodiments, a third antenna is provided between the power connection arm and the second antenna at the upper part of the lower cross arm, and the upper end of the third antenna protrudes upward and backward at the same time. The upper end of the third antenna is higher than the upper end of the second antenna, and the width of the third antenna gradually decreases in the direction from bottom to top.

[0015] In some embodiments, positioning jacks arranged in the front-rear direction are provided at both ends of the housing, fixing pieces are inserted into the positioning jacks, and fixing feet extending out of the housing are provided at the bottom of the fixing pieces.

[0016] The positive effects of the present utility model are as follows: Through the optimized design of the structure of the FPC flexible cable connector, when installing the locking strip, the connecting shafts at both ends of the locking strip are slid into the guide grooves and cross the limit retaining platforms to enter the limit sliding grooves, and the installation of the locking strip is realized through the cooperation of the connecting shafts and the limit sliding grooves. Since the limiting plate has elasticity, the limiting plate can be appropriately deformed when the connecting shaft crosses the limit retaining platform, thereby avoiding the problem of damage to the connecting shaft and fracture of the connecting shaft. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present utility model or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present utility model. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0018] Figure 1 It is a schematic structural diagram of the FPC flexible cable connector in the present utility model;

[0019] Figure 2 For Figure 1Schematic structural diagram of another perspective of the FPC flexible cable connector shown;

[0020] Figure 3 Schematic structural diagram of the housing in the present utility model;

[0021] Figure 4 Cross-sectional view of the FPC flexible cable connector in the present utility model;

[0022] Figure 5 is Figure 4 Partial enlarged view of part A in

[0023] Reference numerals shown in the figure: 1 - housing; 11 - flexible cable socket; 12 - terminal positioning hole; 121 - positioning block; 1211 - second card slot; 122 - fixed jack; 13 - limiting plate; 131 - first card slot; 132 - limiting sliding groove; 133 - connecting shaft; 134 - limiting retaining platform; 14 - positioning jack; 15 - avoidance notch; 16 - positioning jack; 2 - terminal; 21 - upper cross arm; 211 - first antenna; 22 - lower cross arm; 221 - arc groove part; 222 - front stop block; 223 - rear stop block; 224 - second antenna; 225 - third antenna; 226 - power connection arm; 227 - fixed arm; 228 - clamping protrusion; 23 - connecting arm; 3 - locking bar; 31 - abutting arm; 32 - clamping block; 33 - support shaft part; 34 - side baffle; 35 - receiving groove; 4 - fixing piece; 41 - fixing foot. Detailed implementation manners

[0024] Next, the technical solutions in the embodiments of the present utility model will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present utility model. Obviously, the described embodiments are only a part of the embodiments of the present utility model, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present utility model without creative efforts shall fall within the protection scope of the present utility model.

[0025] It should be noted that all directional indications (such as up, down, left, right, front, back...) in the embodiments of the present utility model are only used to explain the relative positional relationship and movement conditions between components in a certain specific posture (as shown in the attached drawings). If the specific posture changes, the directional indications will change accordingly. In the present utility model, unless otherwise clearly specified and defined, terms such as "connection" and "fixation" should be understood in a broad sense. For example, "fixation" can be a fixed connection, a detachable connection, or integrated; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the internal communication of two components or the interaction relationship between two components, unless otherwise clearly defined. For those of ordinary skill in the art, the specific meanings of the above terms in the present utility model can be understood according to specific circumstances.

[0026] In addition, the technical solutions between various embodiments can be combined with each other, but it must be based on the ability of those of ordinary skill in the art to implement. When the combination of technical solutions results in contradictions or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection required by the present utility model.

[0027] The FPC flexible cable connector structure provided by the embodiments of the present utility model is as Figures 1 to 5 shown, which includes a housing 1, terminals 2 and a locking bar 3; a flexible cable socket 11 is provided at the front end of the housing 1; terminal positioning holes 12 are provided on the housing 1, the terminal positioning holes 12 are arranged in the front-rear direction and communicate with the flexible cable socket 11, the terminals 2 are inserted into the terminal positioning holes 12, and the end of the FPC flexible cable is inserted into the flexible cable socket 11, and the gold fingers on the FPC flexible cable are in contact with the terminals 2 to achieve electrical conduction; the terminals 2 include an upper cross arm 21, a lower cross arm 22 and a connecting arm 23, and the upper and lower ends of the connecting arm 23 are respectively integrally connected with the middle parts of the upper cross arm 21 and the lower cross arm 22 to form an I-shaped structure; the locking bar 3 is installed at the rear of the housing 1 and can rotate up and down between a locking angle position and an unlocking angle position, a resisting arm 31 is provided on the locking bar 3, when the locking bar 3 rotates to the locking angle position, the upper end of the rear end of the upper cross arm 21 is pushed upward by the resisting arm 31, so that the front end of the upper cross arm 21 moves downward, so that the front end of the upper cross arm 21 is in reliable contact with the gold fingers on the FPC flexible cable, thereby ensuring the reliability of the connection between the terminals 2 and the FPC flexible cable; when the locking bar 3 is rotated from the locking angle position to the unlocking angle position, the resisting arm 21 releases the resisting limit on the rear end of the upper cross arm 21, so that the front end of the upper cross arm 21 is separated from the gold fingers of the FPC flexible cable, which is beneficial to the extraction of the FPC flexible cable from the flexible cable socket 11 of the FPC flexible cable connector.

[0028] See Figure 2 and Figure 3As shown, the rear parts of both ends of the shell 1 in the length direction are provided with limit plates 13 protruding backwards, the limit plates 13 are elastic, the inner side of the limit plates 13 is provided with a limiting slide groove 132 extending in the front-to-back direction and a limit stopper 134 at the rear side of the limiting slide groove 132, the two ends of the lock bar 3 in the length direction are provided with a connecting shaft 133, the connecting shaft 133 is limited in the limiting slide groove 132, the rear side of the limit stopper 134 is provided with a guide groove for guiding the connecting shaft 133 to pass through, and the front part of the guide groove is close to the limit slide groove 132. A slope surface is formed near the limit stop 134; when installing the lock bar 3, the connecting shafts 133 at both ends of the lock bar 3 are slid into the guide groove and pass over the limit stop 134 along the slope surface into the limit slide groove 132, and the installation of the lock bar 3 is achieved through the cooperation of the connecting shaft 133 and the limit slide groove 132. Since the limit plate 13 is elastic, the limit plate 13 can be deformed to an appropriate amount when the connecting shaft 133 passes over the limit stop 134, thereby avoiding damage to the connecting shaft 133 and the problem of breaking the connecting shaft 133.

[0029] In some embodiments, Figure 1 When the locking bar 3 is in the unlocking angle position, the block 32 is located on the upper side of the limiting plate 13 and is suitable for preventing the locking bar 3 from rotating to the locking angle position through the block 32 and the upper edge of the limiting plate 13; when the locking bar 3 is in the unlocking angle position, the block 32 can be limited to prevent the locking bar 3 from rotating to the locking angle position when subjected to a small external force, thereby preventing malfunction; when the locking bar 3 is in the locking angle position, the block 32 cooperates with the first slot 131 to effectively lock the locking bar 3, thereby ensuring that the locking bar 3 is in the locked position and ensuring the reliability of the connection between the FPC cable and the FPC cable connector; further, by arranging the guide groove and the first slot 131 as the same structure, the structure is simplified.

[0030] In some embodiments, a support shaft portion 33 is provided at the bottom of the locking bar 3 along its length direction, and an arc-shaped groove portion 221 with an opening facing upward is formed at the upper portion of the rear end of the lower cross arm 22, and the support shaft portion 33 is embedded in the arc-shaped groove portion 221, and the contact surface between the support shaft portion 33 and the arc-shaped groove portion 221 is a matching arc-shaped surface.

[0031] See also Figure 4As shown, the upper part of the rear end of the lower cross arm 22 is respectively protruded upward with a front stopper 222 and a rear stopper 223 on the front and rear sides of the arc-shaped groove 221, and the front stopper 222 and the rear stopper 223 are used to form a blocking limit for the support shaft 33 from both sides. The height of the rear stopper 223 is lower than the height of the front stopper 222. The rear stopper 223 is preferably set to a triangle or an arc shape. Such a setting facilitates the support shaft 33 to pass through the rear stopper 223 when the lock bar 3 is installed, making the assembly convenient and quick.

[0032] like Figure 1 and Figure 4 As shown, when the lock bar 3 is in the locked angle position, a receiving groove 35 is formed on the front side, and side baffles 34 are formed at both ends of the receiving groove 35. The upper side wall of the rear end of the shell 1 extends backward to form a convex edge 14 and avoidance gaps 15 are formed at both ends of the convex edge 14. When the lock bar 3 is in the locked angle position, the convex edge 14 is suitable for extending into the receiving groove 35, and the side baffles 34 are correspondingly located in the avoidance gap 15. Such a configuration can reduce the resistance of the rear edge of the shell 1 to the lock bar 3, thereby increasing the opening angle of the lock bar 3 and improving the operational flexibility.

[0033] like Figure 4 and Figure 5 As shown, the front end of the lower cross arm 22 is formed with a power receiving arm 226 and a fixed arm 227 extending forward, a bayonet is formed between the fixed arm 227 and the power receiving arm 226, the front end bottom of the terminal positioning hole 12 is provided with a positioning block 121 and a fixed socket 122 located at the lower side of the positioning block 121, the bayonet is plugged into the positioning block 121, the fixed arm 227 is tightly plugged and fixed in the fixed socket 122, so as to strengthen the positioning effect of the terminal 2, and the bottom of the power receiving arm 226 is provided with a rearward tilting A hook-shaped latching protrusion 228 is obliquely extended, and a second latching groove 1211 cooperating with the latching protrusion 228 is provided on the upper part of the positioning block 121. When the terminal is installed in place, the latching protrusion 228 cooperates with the second latching groove 1211 to form a positioning effect on the terminal 2 to prevent the terminal 2 from sliding backward and loosening; at the same time, the end of the latching protrusion 228 can contact the bottom of the second latching groove 1211 to play an upward elastic support role for the connecting arm 226, thereby enhancing the reliability of the connection between the connecting arm 226 and the FPC cable.

[0034] Furthermore, an upper rear portion of the positioning block 121 is provided with an inclination angle, and the setting of the inclination angle can prevent the positioning block 121 from causing interference with the locking protrusion 228 when the terminal 2 is inserted into the terminal positioning hole 12 .

[0035] like Figure 4 and Figure 5As shown, a first antenna 211 is provided at the lower part of the front end of the upper cross arm 21, and a second antenna 224 is formed at the upper part of the power connection arm 226. The first antenna 211 and the second antenna 224 are in an inverted hook shape and have sharp corners extending into the FPC cable socket 11. With this structural design, after the FPC cable is inserted into the FPC cable socket 11, both the first antenna 211 and the second antenna 224 are in contact with the FPC cable, achieving good conduction performance; moreover, the sharp corners of the first antenna 211 and the second antenna 224 can bite the gold fingers on the FPC cable, enhancing the connection strength.

[0036] Continue to refer to Figure 4 As shown, a third antenna 225 is provided between the power connection arm 226 and the second antenna 224 at the upper part of the lower cross arm 22. After the FPC cable connector is inserted into the FPC cable socket 11, it contacts the FPC cable through the third antenna 225 to increase the contact points and improve the electrical conduction performance. The upper end of the third antenna 225 protrudes upward and backward at the same time, and the upper end of the third antenna 225 is higher than the upper end of the second antenna 224. This can ensure effective contact between the third antenna 224 and the FPC cable while reducing the interference of the third antenna 224 during the insertion of the FPC cable into the FPC cable socket 11. Further, the width of the third antenna 225 gradually decreases in the direction from bottom to top, which can enhance the anti-deformation ability of the third antenna 225 and keep its good resilience.

[0037] As Figure 1 As shown, positioning jacks 16 are provided at both ends of the housing 1 in the front-rear direction. Fixing pieces 4 are inserted into the positioning jacks 16. A fixing leg 41 extending out of the housing 1 is provided at the bottom of the fixing piece 4. When the FPC cable connector is mounted on the circuit board, the rear end of the terminal 2 is welded to the welding position on the circuit board to achieve electrical connection; at the same time, the fixing leg 41 is welded to the welding position on the circuit board to strengthen the fixed connection between the FPC cable connector and the circuit board.

[0038] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. An FPC cable connector, comprising a housing (1), a terminal (2) and a locking bar (3); The front end of the housing (1) is provided with a cable socket (11); The housing (1) is provided with a terminal positioning hole (12), the terminal positioning hole (12) is communicated with the wiring socket (11), and the terminal (2) is plugged into the terminal positioning hole (12); The terminal (2) comprises an upper cross arm (21), a lower cross arm (22) and a connecting arm (23); the upper and lower ends of the connecting arm (23) are respectively connected to the middle of the upper cross arm (21) and the lower cross arm (22) as a whole; The lock bar (3) is mounted on the rear part of the housing (1) and can rotate up and down between a locking angle position and an unlocking angle position. A resisting arm (31) is provided on the lock bar (3). When the lock bar (3) rotates toward the locking angle position, the resisting arm (31) pushes the rear end of the upper cross arm (21) to move upward, so that the front end of the upper cross arm (21) moves downward. It is characterized in that The shell (1) is provided with a limit plate (13) protruding backward at the rear of both ends in the length direction, and the limit plate (13) is elastic. The inner side of the limit plate (13) is provided with a limit slide groove (132) extending in the front-to-back direction and a limit stop platform (134) located at the rear side of the limit slide groove (132). The lock bar (3) is provided with a connecting shaft (133) at both ends in the length direction, and the connecting shaft (133) is limited in the limiting slide groove (132). The rear side of the limit stop platform (134) is provided with a guide groove for guiding the connecting shaft (133) to pass through, and the front part of the guide groove is formed with a slope surface near the limit stop platform (134).

2. The FPC flexible cable connector according to claim 1, wherein, Blocks (32) are provided on both ends of the locking bar (3), and a first slot (131) is provided on the inner wall of the limiting plate (13). When the locking bar (3) is in a locking angle position, the block (32) is engaged with the first slot (131). When the locking bar (3) is in an unlocking angle position, the block (32) is located on the upper side of the limiting plate (13) and is suitable for preventing the locking bar (3) from rotating to the locking angle position by forming a contact interference with the upper edge of the limiting plate (13). The guide groove and the first slot (131) have the same structure.

3. The FPC cable connector according to claim 1, wherein The bottom of the locking bar (3) is provided with a supporting shaft portion (33) arranged along its length direction; the upper portion of the rear end of the lower cross arm (22) forms an arc-shaped groove portion (221) with an opening facing upward; the supporting shaft portion (33) is embedded in the arc-shaped groove portion (221); and the contact surface between the supporting shaft portion (33) and the arc-shaped groove portion (221) is a matching arc-shaped surface.

4. The FPC flexible cable connector according to claim 3, wherein, A front stopper (222) and a rear stopper (223) are respectively protruded upwards at the upper rear end of the lower cross arm (22) on both front and rear sides of the arc-shaped groove (221), and the height of the rear stopper (223) is lower than that of the front stopper (222).

5. The FPC flexible cable connector according to claim 1, characterized in that On the front side of the locking bar (3) at the locked angular position, a receiving groove (35) is formed. Side baffles (34) are formed at both ends of the receiving groove (35). At the upper rear side wall of the housing (1), a convex edge (14) extends rearward, and avoiding notches (15) are formed at both ends of the convex edge (14). When the locking bar (3) is at the locked angular position, the convex edge (14) is adapted to extend into the receiving groove (35), and the side baffles (34) are correspondingly located within the avoiding notches (15).

6. The FPC cable connector according to claim 1, characterized in that, At the front end of the lower cross arm (22), a power connection arm (226) and a fixing arm (227) that extend forward are formed. A bayonet is formed between the fixing arm (227) and the power connection arm (226). At the bottom of the front end of the terminal positioning hole (12), a positioning block (121) and a fixing jack (122) located below the positioning block (121) are provided. The bayonet is inserted into the positioning block (121), and the fixing arm (227) is tightly inserted and fixed within the fixing jack (122). Moreover, at the bottom of the power connection arm (226), a locking projection (228) that extends rearward in an inclined manner and forms a hook shape is provided. At the upper part of the positioning block (121), a second card slot (1211) that cooperates with the locking projection (228) is provided.

7. The FPC cable connector according to claim 6, wherein At the upper rear side of the positioning block (121), an inclined angle is provided.

8. The FPC flexible cable connector according to claim 6, wherein At the lower front part of the upper cross arm (21), a first antenna (211) is provided. At the upper part of the power connection arm (226), a second antenna (224) is formed. The first antenna (211) and the second antenna (224) are in an inverted hook shape structure and have a sharp angle extending into the wire arranging socket (11).

9. The FPC flexible cable connector according to claim 8, wherein, At the upper part of the lower cross arm (22) between the power connection arm (226) and the second antenna (224), a third antenna (225) is provided. Moreover, the upper end of the third antenna (225) protrudes upward and simultaneously protrudes rearward. The upper end of the third antenna (225) is higher than the upper end of the second antenna (224), and in the direction from bottom to top, the width of the third antenna (225) gradually decreases.

10. The FPC flexible cable connector according to claim 1, wherein, At both ends of the housing (1), positioning jacks (16) arranged in the front-rear direction are provided. Fixing pieces (4) are inserted into the positioning jacks (16). At the bottom of the fixing piece (4), fixing feet (41) that extend out of the housing (1) are provided.

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