CROSS-REFERENCE TO RELATED APPLICATION 
     The present application claims priority to and the benefit of Korean Patent Application No. 10-2015-0171003 filed on Dec. 2, 2015, the entire contents of which is incorporated herein for all purposes by this reference. 
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to an automatic transmission for a vehicle. 
     Description of Related Art 
     Recent increases in oil prices are triggering hard competition in enhancing fuel consumption of a vehicle. 
     In this sense, research on an engine has been undertaken to achieve weight reduction and to enhance fuel consumption by so-called downsizing, and research on an automatic transmission has been performed to simultaneously provide better drivability and fuel consumption by achieving more shift stages. 
     In order to achieve more shift stages for an automatic transmission, the number of parts is typically increased, which may deteriorate installability, production cost, weight, and/or power flow efficiency. 
     Therefore, in order to maximally enhance fuel consumption of an automatic transmission having more shift stages, it is important for better efficiency to be derived by a smaller number of parts. 
     The information disclosed in this Background of the Invention section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any thrill of suggestion that this information forms the prior art already known to a person skilled in the art. 
     BRIEF SUMMARY 
     Various aspects of the present invention are directed to providing a planetary gear train of an automatic transmission for a vehicle having advantages of, by minimal complexity, realizing at least forward eight speeds and at least one reverse speed, thereby improving power delivery performance and fuel consumption due to multi-stages, and improving driving stability of a vehicle by utilizing a low rotation speed of an engine. 
     An exemplary planetary gear set according to an embodiment includes an input shaft for receiving an engine torque, an output shaft for outputting a shifted torque, a first planetary gear set having first, second, and third rotational elements, a second planetary gear set having fourth, fifth, and sixth rotational elements, a third planetary gear set having seventh, eighth, and ninth rotational elements, and six control elements for selectively interconnecting the rotational elements. 
     The exemplary planetary gear set may further include a first connecting member fixedly connected with the first rotational element and the fifth rotational element, and selectively connectable with the input shaft, a second connecting member fixedly connected with the second rotational element, a third connecting member fixedly connected with the third rotational element and the eighth rotational element and fixedly connected with the output shaft, a fourth connecting member fixedly connected with the fourth rotational element and the transmission housing, and selectively connectable with the second connecting member, a fifth connecting member fixedly connected with the sixth rotational element and selectively connected with the third connecting member, a sixth connecting member fixedly connected with the seventh rotational element and selectably connectable to the input shaft, and a seventh connecting member fixedly connected with the ninth rotational element and selectively connectable with the second connecting member and the fifth connecting member. 
     The first planetary gear set may be a single pinion planetary gear set, where the first rotational element is a first sun gear, the second rotational element is a first planet carrier, and the third rotational element is a first ring gear. The second planetary gear set may be a single pinion planetary gear set, where the fourth rotational element is a second sun gear, the fifth rotational element is a second planet carrier, and the sixth rotational element is a second ring gear. The third planetary gear set may be a single pinion planetary gear set, where the seventh rotational element is a third sun gear, the eighth rotational element is a third planet carrier, and the ninth rotational element is a third ring near. 
     The six control elements may include a first clutch selectively connecting the input shaft and the first connecting member, a second clutch selectively connecting the input shaft and the sixth connecting member, a third clutch selectively connecting the fifth connecting member and the seventh connecting member, a fourth clutch selectively connecting the second connecting member and the fourth connecting member, a fifth clutch selectively connecting the second connecting member and the seventh connecting member, and a sixth clutch selectively connecting the third connecting member and the fifth connecting member. 
     Shift stages realized by selective operation of three control elements among the six control elements may include a forward first speed formed by simultaneous operation of the second, fourth, and sixth clutches, a forward second speed formed by simultaneous operation of the second, fourth, and fifth clutches, a forward third speed formed by simultaneous operation of the second, fifth, and sixth clutches, a forward fourth speed formed by simultaneous operation of the second, third, and fifth clutches, a forward fifth speed formed by simultaneous operation of the first, second, and fifth clutches, a forward sixth speed formed by simultaneous operation of the first, second, and sixth clutches, a forward seventh speed formed by simultaneous operation of the first, third, and sixth clutches, a forward eighth speed formed by simultaneous operation of the first, fifth, and sixth clutches, and a reverse speed formed by simultaneous operation of the first, fourth, and sixth clutches. 
     A planetary gear train according to an exemplary embodiment of the present invention may realize at least forward eighth speeds and at least one reverse speed formed by operating the three planetary gear sets as simple planetary gear sets by controlling six control elements. 
     In addition, a planetary gear train according to an exemplary embodiment of the present invention may substantially improve driving stability by realizing shift stages appropriate for rotation speed of an engine due to multi-stages of an automatic transmission. 
     In addition, a planetary gear train according to an exemplary embodiment of the present invention may maximize engine driving efficiency by multi-stages of an automatic transmission, and may improve power delivery performance and fuel consumption. 
     Further, effects that can be obtained or expected from exemplary embodiments of the present invention are directly or suggestively described in the following detailed description. That is, various effects expected from exemplary embodiments of the present invention will be described in the following detailed description. 
     The methods and apparatuses of the present invention have other features and advantages which will be apparent from or are set forth in more detail in the accompanying drawings, which are incorporated herein, and the following Detailed Description, which together serve to explain certain principles of the present invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of a planetary gear train according to an exemplary embodiment of the present invention. 
         FIG. 2  is an operational chart for respective control elements at respective shift stages in a planetary gear train according to an exemplary embodiment of the present invention. 
     
    
    
     It should be understood that the appended drawings are not necessarily to scale, presenting a somewhat simplified representation of various features illustrative of the basic principles of the invention. The specific design features of the present invention as disclosed herein, including, for example, specific dimensions, orientations, locations, and shapes will be determined in part by the particular intended application and use environment. 
     In the figures, reference numbers refer to the same or equivalent parts of the present invention throughout the several figures of the drawing. 
     DETAILED DESCRIPTION 
     Reference will now be made in detail to various embodiments of the present invention(s), examples of which are illustrated in the accompanying drawings and described below. While the invention(s) will be described in conjunction with exemplary embodiments, it will be understood that the present description is not intended to limit the invention(s) to those exemplary embodiments. On the contrary, the invention(s) is/are intended to cover not only the exemplary embodiments, but also various alternatives, modifications, equivalents and other embodiments, which may be included within the spirit and scope of the invention as defined by the appended claims. 
     The present invention will be described more fully hereinafter with reference to the accompanying drawings, in which exemplary embodiments of the invention are shown. As those skilled in the art would realize, the described embodiments may be modified in various different ways, all without departing from the spirit or scope of the present invention. 
     The drawings and description are to be regarded as illustrative in nature and not restrictive, and like reference numerals designate like elements throughout the specification. 
     In the following description, dividing names of components into first, second, and the like is to divide the names because the names of the components are the same as each other and an order thereof is not particularly limited. 
       FIG. 1  is a schematic diagram of a planetary gear train according to an exemplary embodiment of the present invention. 
     Referring to  FIG. 1 , a planetary gear train according to an exemplary embodiment of the present invention includes first, second, and third planetary gear sets PG 1 , PG 2 , and PG 3  arranged on a same axis, an input shaft IS, an output shaft OS, seven connecting members TM 1  to TM 7  connected with rotational elements of the first, second, and third planetary gear sets PG 1 , PG 2 , and PG 3 , six control elements C 1  to C 6 , and a transmission housing H. 
     Torque input from the input shaft IS is shifted by cooperative operation of the first, second, and third planetary gear sets PG 1 , PG 2 , and PG 3 , and then output through the output shaft OS. 
     The simple planetary gear sets are arranged in the order of first, first, second, and third planetary gear sets PG 1 , PG 2 , and PG 3 , from an engine side. 
     The input shaft IS is an input member and the torque from a crankshaft of an engine, after being torque-converted through a torque converter, is input into the input shaft IS. 
     The output shaft OS is an output member, and being arranged on a same axis as the input shaft IS, delivers a shifted torque to a drive shaft through a differential apparatus. 
     The first planetary gear set PG 1  is a single pinion planetary gear set, and includes a first sun gear S 1 , a first planet carrier PC 1  that supports a first pinion P 1  externally engaged with the first sun gear S 1 , and a first ring gear R 1  internally engaged with the first pinion P 1 . The first sun gear S 1  acts as a first rotational element N 1 , the first planet carrier PC 1  acts as a second rotational element N 2 , and the first ring gear R 1  acts as a third rotational element N 3 . 
     The second planetary gear set PG 2  is a single pinion planetary gear set, and includes a second sun gear S 2 , a second planet carrier PC 2  that supports a second pinion P 2  externally engaged with the second sun gear S 2 , and a second ring gear R 2  internally engaged with the second pinion P 2 . The second sun gear S 2  acts as a fourth rotational element N 4 , the second planet carrier PC 2  acts as a fifth rotational element N 5 , and the second ring gear R 2  acts as a sixth rotational element N 6 . 
     The third planetary gear set PG 3  is a single pinion planetary gear set, and includes a third sun gear S 3 , a third planet carrier PC 3  that supports a third pinion P 3  externally engaged with the third sun gear S 3 , and a third ring gear R 3  internally engaged with the third pinion P 3 . The third sun gear S 3  acts as a seventh rotational element N 7 , the third planet carrier PC 3  acts as an eighth rotational element N 8 , and the third ring gear R 3  acts as a ninth rotational element N 9 . 
     In the arrangement of the first, second, and third planetary gear sets PG 1 , PG 2 , and PG 3 , the first rotational element N 1  is directly connected with the fifth rotational element N 5 , and the third rotational element N 3  is directly connected with the eighth rotational element N 8 , by seven connecting members TM 1  to TM 7 . 
     The seven connecting members TM 1  to TM 7  are arranged as follows. 
     The first connecting member TM 1  is connected with the first rotational element N 1  (first sun gear S 1 ) and the fifth rotational element N 5  (second planet carrier PC 2 ), and selectively connectable with the input shaft IS. 
     The second connecting member TM 2  is connected with second rotational element N 2  (first planet carrier PC 1 ). 
     The third connecting member TM 3  is connected with the third rotational element N 3  (first ring gear R 1 ) and the eighth rotational element N 8  (third planet carrier PC 3 ), and directly connected with the output shaft OS. 
     The fourth connecting member TM 4  is connected with the fourth rotational element N 4  (second sun gear S 2 ), directly connected with the transmission housing H, and selectively connectable with the second connecting member TM 2 . 
     The fifth connecting member TM 5  is connected with the sixth rotational element N 6  (second ring gear R 2 ), and selectively connectable with the third connecting member TM 3 . 
     The sixth connecting member TM 6  is connected with the seventh rotational element N 7  (third sun gear S 3 ), and directly connected with the input shaft IS. 
     The seventh connecting member TM 7  is connected with the ninth rotational element N 9  (third ring gear R 3 ), and selectively connectable with the second connecting member TM 2  and the fifth connecting member TM 5 . 
     The connecting members TM 1  to TM 7  may be selectively interconnected with one another by control elements of six clutches C 1 , C 2 , C 3 , C 4 , C 5 , and C 6 . 
     The six control elements C 1  to C 6  are arranged as follows. 
     The first clutch C 1  is arranged between the input shaft IS and the first connecting member TM 1 , such that the input shaft IS and the first connecting member TM 1  may selectively become integral. 
     The second clutch C 2  is arranged between the input shaft IS and the sixth connecting member TM 6 , such that the input shaft IS and the sixth connecting member TM 6  may selectively become integral. 
     The third clutch C 3  is arranged between the fifth connecting member TM 5  and the seventh connecting member TM 7 , such that the fifth connecting member TM 5  and the seventh connecting member TM 7  may selectively become integral. 
     The fourth clutch C 4  is arranged between the second connecting member TM 2  and the fourth connecting member TM 4 , such that the second connecting member TM 2  and the fourth connecting member TM 4  may selectively become integral. 
     The fifth clutch C 5  is arranged between the second connecting member TM 2  and the seventh connecting member TM 7 , such that the second connecting member TM 2  and the seventh connecting member TM 7  may selectively become integral. 
     The sixth clutch C 6  is arranged between the third connecting member TM 3  and the fifth connecting member TM 5 , such that the third connecting member TM 3  and the fifth connecting member TM 5  may selectively become integral. 
     Respective control elements of the first, second, third, fourth, fifth, and sixth clutches C 1 , C 2 , C 3 , C 4 , C 5 , and C 6  may be realized as multi-plate hydraulic pressure friction devices that are frictionally engaged by hydraulic pressure. 
       FIG. 2  is an operational chart for respective control elements at respective shift stages in a planetary gear train according to an exemplary embodiment of the present invention. 
     As shown in  FIG. 2 , a planetary gear train according to an exemplary embodiment of the present invention performs shifting by operating three control elements at respective shift stages. 
     In the forward first speed shift stage D 1 , the second, fourth, and sixth clutches C 2 , C 4 , and C 6  are simultaneously operated. As a result, the input shaft IS and the sixth connecting member TM 6  are interconnected by the operation of the second clutch C 2 , and the second connecting member TM 2  and the fourth connecting member TM 4  are interconnected by the operation of the fourth clutch C 4 , and the third connecting member TM 3  and the fifth connecting member TM 5  are interconnected by the operation of the sixth clutch C 6 . In this state, torque is input to the sixth connecting member TM 6 . In addition, the fourth connecting member TM 4  acts as a fixed element, and the second connecting member TM 2  simultaneously acts as a fixed element by the operation of the fourth clutch C 4 , thereby realizing the forward first speed and outputting a shifted torque to the output shaft OS through the third connecting member TM 3 . 
     In the forward second speed shift stage D 2 , the second, fourth, and fifth clutches C 2 , C 4 , and C 5  are simultaneously operated. As a result, the input shaft IS and the sixth connecting member TM 6  are interconnected by the operation of the second clutch C 2 , and the second connecting member TM 2  and the fourth connecting member TM 4  are interconnected by the operation of the fourth clutch C 4 , and the second connecting member TM 2  and the seventh connecting member TM 7  are interconnected by the operation of the fifth clutch C 5 . In this state, torque is input to the sixth connecting member TM 6 . In addition, the fourth connecting member TM 4  acts as a fixed element, and the second connecting member TM 2  simultaneously acts as a fixed element by the operation of the fourth clutch C 4 , thereby realizing the forward second speed and outputting a shifted torque to the output shaft OS through the third connecting member TM 3 . 
     In the forward third speed shift stage D 3 , the second, fifth, and sixth clutches C 2 , C 5 , and C 6  are simultaneously operated. As a result, the input shaft IS and the sixth connecting member TM 6  are interconnected by the operation of the second clutch C 2 , and the second connecting member TM 2  and the seventh connecting member TM 7  are interconnected by the operation of the fifth clutch C 5 , and the third connecting member TM 3  and the fifth connecting member TM 5  are interconnected by the operation of the sixth clutch C 6 . In this state, torque is input to the sixth connecting member TM 6 . In addition, the fourth connecting member TM 4  acts as a fixed element, thereby realizing the forward third speed and outputting a shifted torque to the output shaft OS through the third connecting member TM 3 . 
     In the forward fourth speed shift stage D 4 , the second, third, and fifth clutches C 2 , C 3 , and C 5  are simultaneously operated. As a result, the input shaft IS and the sixth connecting member TM 6  are interconnected by the operation of the second clutch C 2 , and the fifth connecting member TM 5  and the seventh connecting member TM 7  are interconnected by the operation of the third clutch C 3 , and the second connecting member TM 2  and the seventh connecting member TM 7  are interconnected by the operation of the fifth clutch C 5 . In this state, torque is input to the sixth connecting member TM 6 . In addition, the fourth connecting member TM 4  acts as a fixed element, thereby realizing the forward fourth speed and outputting a shifted torque to the output shaft OS through the third connecting member TM 3 . 
     In the forward fifth speed shift stage D 5 , the first, second, and fifth clutches C 1 , C 2 , and C 5  are simultaneously operated. As a result, the input shaft IS and the first connecting member TM 1  are interconnected by the operation of the first clutch C 1 , and the input shaft IS and the sixth connecting; member TM 6  are interconnected by the operation of the second clutch C 2 , and the second connecting member TM 2  and the seventh connecting member TM 7  are interconnected by the operation of the fifth clutch C 5 . In this state, torque is input to the first and sixth connecting members TM 1  and TM 6 . In addition, the fourth connecting member TM 4  acts as a fixed element, thereby realizing the forward fifth speed that outputs a same torque as inputted, and the input torque is output to the output shaft OS through the third connecting member TM 3 . 
     In the forward sixth speed shift stage D 6 , the first, second, and sixth clutches C 1 , C 2 , and C 6  are simultaneously operated. As a result, the input shaft IS and the first connecting member TM 1  are interconnected by the operation of the first clutch C 1 , and the input shaft IS and the sixth connecting member TM 6  are interconnected by the operation of the second clutch C 2 , and the third connecting member TM 3  and the fifth connecting member TM 5  are interconnected by the operation of the sixth clutch C 6 . In this state, torque is input to the first and sixth connecting members TM 1  and TM 6 . In addition, the fourth connecting member TM 4  acts as a fixed element, thereby realizing the forward sixth speed and outputting a shifted torque to the output shaft OS through the third connecting member TM 3 . 
     In the forward seventh speed shift stage D 7 , the first, third, and sixth clutches C 1 , C 3 , and C 6  are simultaneously operated. As a result, the input shaft IS and the first connecting member TM 1  are interconnected by the operation of the first clutch C 1 , and the fifth connecting member TM 5  and the seventh connecting member TM 7  are interconnected by the operation of the third clutch C 3 , and the third connecting member TM 3  and the fifth connecting member TM 5  are interconnected by the operation of the sixth clutch C 6 . In this state, torque is input to the first connecting member TM 1 . In addition, the fourth connecting member TM 4  acts as a fixed element, thereby realizing the forward seventh speed and outputting a shifted torque to the output shaft OS through the third connecting member TM 3 . 
     In the forward eighth speed shift stage D 8 , the first, fifth, and sixth clutches C 1 , C 5 , and C 6  are simultaneously operated. As a result, the input shaft IS and the first connecting member TM 1  are interconnected by the operation of the first clutch C 1 , and the second connecting member TM 2  and the seventh connecting member TM 7  are interconnected by the operation of the fifth clutch C 5 , and the third connecting member TM 3  and the fifth connecting member TM 5  are interconnected by the operation of the sixth clutch C 6 . In this state, torque is input to the first connecting member TM 1 . In addition, the fourth connecting member TM 4  acts as a fixed element, thereby realizing the forward eighth speed and outputting a shifted torque to the output shaft OS through the third connecting member TM 3 . 
     In the reverse speed REV, the first, fourth, and sixth clutches C 1 , C 4 , and C 6  are simultaneously operated. As a result, the input shaft IS and the first connecting member TM 1  are interconnected by the operation of the first clutch C 1 , and the second connecting member TM 2  and the fourth connecting member TM 4  are interconnected by the operation of the fourth clutch C 4 , and the third connecting member TM 3  and the fifth connecting member TM 5  are interconnected by the operation of the sixth clutch C 6 . In this state, torque is input to the first connecting member TM 1 . In addition, the fourth connecting member TM 4  acts as a fixed element, and the second connecting member TM 2  simultaneously acts as a fixed element by the operation of the fourth clutch C 4 , thereby realizing the reverse speed and outputting a shifted torque to the output shaft OS through the third connecting member TM 3 . 
     As described above, a planetary gear train according to an exemplary embodiment of the present invention may achieve at least eight forward speeds and at least one reverse speed formed by operating three planetary gear sets PG 1 , PG 2 , and PG 3  by controlling six clutches C 1 , C 2 , C 3 , C 4 , C 5 , and C 6 . 
     In addition, a planetary gear train according to an exemplary embodiment of the present invention may substantially improve driving stability by realizing shift stages appropriate for rotation speed of an engine due to multi-stages of an automatic transmission. 
     In addition, a planetary gear train according to an exemplary embodiment of the present invention may maximize engine driving efficiency by multi-stages of an automatic transmission, and may improve power delivery performance and fuel consumption. 
     For convenience in explanation and accurate definition in the appended claims, the terms “upper”, “lower”, “inner” and “outer” are used to describe features of the exemplary embodiments with reference to the positions of such features as displayed in the figures. 
     The foregoing descriptions of specific exemplary embodiments of the present invention have been presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed, and obviously many modifications and variations are possible in light of the above teachings. The exemplary embodiments were chosen and described in order to explain certain principles of the invention and their practical application, to thereby enable others skilled in the art to make and utilize various exemplary embodiments of the present invention, as well as various alternatives and modifications thereof. It is intended that the scope of the invention be defined by the Claims appended hereto and their equivalents.
Nine or more forward speeds and at least one reverse speed are achieved by a planetary gear train of an automatic transmission for a vehicle including an input shaft, an output shaft, three planetary gear sets respectively having three rotational elements, and six control elements for selectively interconnecting the rotational elements.