a systematic approach for the structural synthesis of

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A Systematic Approach for the Structural Synthesis of

Differential-Type South Pointing Chariots∗

Hong-Sen YAN∗∗ and Chun-Wei CHEN∗∗

South Pointing Chariot is one of the important mechanical inventions in ancient China. Itachieves the purpose of fixing direction by applying mechanical devices. All existing designscan be classified into two types: “fixed-axis type” and “differential type”. In this study, firstly,the existing designs are analyzed and decomposed into four parts: two inputs, a transmissionpart, a passive feedback mechanism, and one output. Secondly, because some existing de-signs have the same topological structures, new representations are used to identify differentaxial directions of joints and characteristics of members. Thirdly, a design methodology isproposed to systematically synthesize all feasible design concepts of differential-type SouthPointing Chariots. Finally, three examples are provided.

Key Words: South-Pointing Chariot, Structural Synthesis, Mechanism Design, History ofMachinery

1. Introduction

There were many mechanical inventions in ancientChina, but now few people know about these achieve-ments due to a lack of surviving objects and literature.South Pointing Chariot ( ) is a typical example. Inearly days, people sometimes confused South PointingChariot with the compass, and they believed that SouthPointing Chariot was just a magnet hidden inside. In fact,South Pointing Chariot should be called “a fixed direc-tion chariot” in the functional aspect, since it achieves thepurpose of fixing direction based on mechanism devices.So far, no relative ancient objects or archaeological relicshave been found, and no literature clearly provides the in-terior mechanism designed in ancient times.

In the 18th century, scholars began to pay attentionto this topic and started studying and proving the exis-tence of South Pointing Chariot in ancient China. In 1732,Gaubil(1) and other scholars in Europe assumed that SouthPointing Chariot was equal to the compass. In 1834,Klaproth(2) misunderstood and translated “South Point-ing Chariot” into “Char Magnetique”. In 1908, Hirth(3)

doubted the feasibility of controlling the output to fix thesame direction by several gears. In 1909, Giles(4) trans-lated two paragraphs of descriptions about South Point-

∗ Received 26th December, 2005 (No. 05-5135)∗∗ Department of Mechanical Engineering, National Cheng

Kung University, 1 University Road, Tainan 701–01,Taiwan, R.O.C. E-mail: [email protected]

ing Chariots in Song-Shi ( , The book of Song dy-nasty) into English but failed in manufacturing the model.In 1925, Moule(5) retranslated into a more exact versionand successfully reconstructed Yan Su’s South PointingChariot ( ) invented in Song Dynasty. In 1937,Wang(6) arranged historical records of ancient China andreconstructed Yan Su’s South Pointing Chariot. Accord-ing to another hypothetical structure, in 1947, Lanch-ester(7) proposed a South Pointing Chariot with a dif-ferential mechanism. Thereafter, Needham(8), Li(9) andLu(10) summarized the studies of South Pointing Chariotand some scholars focused on designing different interiormechanisms(11) – (19).

In 1994, Lu(10) classified South Pointing Chariotsinto two types: fixed-axis-type and differential-type. Thefixed-axis type South Pointing Chariots are close to the de-scriptions of the historical records in Song Shi, and the de-gree of freedom is one. But this type is difficult to control.Differential-type South Pointing Chariots provide betterperformance and accuracy, and the degrees of freedom aretwo. However, we have not discovered this kind of designor relative application in ancient China.

The major purpose of this paper is to synthesize allpossible topological structures of differential-type SouthPointing Chariots. In the 1960’s, some pioneer schol-ars(20) – (22) applied the concept from graph theory for ana-lyzing and synthesizing the topological structure of mech-anisms. And, Yan(23) – (26) proposed a methodology for thesystematic generation of all possible design concepts sub-

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ject to design requirements and constraints.In what follows, the historical background and

records of the South Pointing Chariot is introduced first.Next, representations for describing the topological struc-tures of existing designs to show the relationships betweenthe inputs and the output are given. Then, a design ap-proach for the systematic generation of all possible designconcepts of the differential-type South Pointing Chariotsis provided. Finally, three design examples are given toverify the proposed design process.

2. Historical Background and Records

According to legend, it was said that both Huang-Di( ) and Zhou-Gong ( ) successfully invented SouthPointing Chariots around 3000–5000 years ago. But theywere not recorded in the official literature and there wasnot enough evidence to support the argument.

This work searched for the descriptions regarding de-sign and manufacture of South Pointing Chariots in offi-cial literatures of ancient China from the period of ThreeKingdoms (220–280 AD) to the Jin Dynasty (1115–1234AD). Over 20 ancient books mentioned the chariots. Theresults show that South Pointing Chariot was successfullydesigned and manufactured many times during the 3rd tothe 13th centuries AD. According to the official records,South Pointing Chariot firstly appeared in the period ofthe Three Kingdoms(27). There were two detailed recordsabout interior mechanism in Song-Shi(28), including exte-rior shape, dimensions, and numbers of teeth.

The development of South Pointing Chariots was notimproved continuously from any existing designs. Thedesigns which appeared in the different dynasties shouldhave been invented independently. The objects were al-ways destroyed or lost in the flames of wars during thechange of dynasties. It is a pity that no records or objectswere found after Yuan Dynasty (1206–1368 AD). There-fore, we are not able to assure exactly the structure ofmechanisms of South Pointing Chariots in ancient China.

3. Analysis of Existing Designs

Existing designs of South Pointing Chariots can bedivided into four parts: two inputs, a transmission part, apassive feedback mechanism, and one output(29).

3. 1 InputsAccording to the historical records of ancient China,

South Pointing Chariots had two wheels as the inputs.When the chariot makes a straight-line motion, the two in-puts have the same angular velocity and the body fixes thedirection. When the chariot turns left or right, the angularvelocities of the two inputs are different, and it causes thebody to rotate.

3. 2 Transmission partThe transmission part connects the two inputs and the

passive feedback mechanism. There are two types: one

(a) Different existing designs(7), (18)

(b) Corresponding passive feedback mechanisms

(c) The same generalized chain

Fig. 1 Two existing designs with the same generalized chain

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is to connect the input member with wheel directly, suchas the design of Yan(12). The other is to add some com-ponents for transmitting motions, such as the design ofMuneharu(16).

3. 3 Passive feedback mechanismThe passive feedback mechanism is the main part of

a South Pointing Chariot. In the fields of cybernetics andnatural science, there are two types of feedback: “posi-tive feedback” and “passive (negative) feedback”. The for-mer enlarges the input signals, and the latter balances thewhole system. The passive feedback mechanism receivesthe two inputs, and outputs the same rotational angle ofthe carriage in the opposite direction. From this perspec-tive, Needham(8) suggests that South Pointing Chariot wasthe first cybernetic device in the world.

3. 4 OutputThe output is a member of the passive feedback

mechanism to show the fixed direction. According to thehistorical records of ancient China, there was a woodenperson on the output link, and its finger pointed to the de-sire fixed direction.

Through analysis procedure, we obtain the topolog-ical characteristics of South Pointing Chariots based onavailable existing designs. The mechanical componentsinclude linkages(5) – (7), (11) – (19), gears(5) – (7), (11) – (19), ropesand pulleys(5), (6), (19), and frictional wheels(19).

Many different designs have the same topologicalstructures after the process of generalization(24) – (29), e.g.,Lanchester’s(7) design and Hsieh’s(18) design as shown inFig. 1. Other designs are based on the same generalizedchain with different members as inputs and output. Fur-thermore, different models are also obtained by replacingdifferent type of gears and designing different transmis-sion parts. Therefore, representations are needed to showdetailed information and discriminate between differentdesigns.

4. Representation of Joints and Members

In the past years, several representations for the jointsand members of kinematic chains were developed for thestructural analysis and synthesis of mechanisms. Yan andLiu(30) introduced the concept of joint-codes for simplify-ing the topology matrices and graphs for mechanisms withvariable topologies. Yan and Kuo(31) further presented thetopological representations and characteristics for kine-matic joints that are capable of topological variation in amechanism with variable topology. Here, we propose rep-resentations to identify the joints and members in gener-alized chains of differential-type South Pointing Chariotsfor mechanisms with fixed topology.

From the results of analysis, we conclude that all axialdirections of revolute pairs in existing mechanisms are ei-ther horizontal or vertical to the ground. For non-revolutepairs, there are three connecting types: perpendicular, in-

(a) Lanchester’s design(7) (b) Hsieh’s design(18)

Fig. 2 Generalized chains of Lanchester’s and Hsieh’s designswith new representations

ternal, and external. The representation of joints is as fol-lows:

J characteristic of jointtype of joint

in which the subscript denotes the type of joint and the su-perscript denotes the characteristic of the joint. For revo-lute pairs, there are two characteristics: vertical (V) or hor-izontal (H) to the ground. For non-revolute pairs, there arethree types: the joint is incident to two members with per-pendicular axial direction (B), the joint is incident to twomembers with parallel axial direction and external con-nection (SE) or internal connection (SI), respectively. Forexamples, the joint is denoted as JV

R to represent that theaxial direction of a revolute joint is vertical to the ground,and the joint is denoted as JB

G to represent that the charac-teristic of a gear pair is incident to two gears whose axialdirections are perpendicular to each other.

Although the passive feedback mechanism is the keyin a South Pointing Chariot, the design of the inputs,the output, and the transmission part are also concernedwith the final results. In fact, some existing designs havethe same passive feedback mechanism but with differentinputs, transmission part, and output. This informationshould be included in the topological structure. And, therepresentation of members is as follows:

K input / output, type of transmission parttype of member

in which the subscript denotes the type of members andthe superscript denotes the input/output and type of trans-mission part. For examples, the joint denoted as KI1,G

G rep-resents that there is a gear as the input 1 and the transmis-sion part is composed of gears, and the joint denoted asKI2,D

O represents that there is a roller as the input 2 and itconnects with the wheel directly.

Figure 2 (a) and (b) shows the corresponding gener-alized chain of Lanchester’s design and Hsieh’s design,respectively. The advantage of the representation of jointsand members is that the designer can transform all feasibledesigns into different generalized chains in the process ofanalysis and reserve the information of inputs, output, andtransmission part. Such representations are also useful tosynthesize all possible design concepts of South PointingChariots systematically.


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Fig. 3 Design procedure

5. Design Process

Figure 3 shows the design procedure for synthesizingthe topological structure of South Pointing Chariots withdifferential-type. It consists of the following 5 steps:Step 1 Specifications

After studying available literature and analyzing allexisting designs, we recognize that the numbers of mem-bers in the passive feedback mechanism of the recon-struction designs are different. The mechanisms of SouthPointing Chariots have various components in each dy-nasty based on the ancient science theories and technolo-gies of that time. Therefore, the first step of the designprocess is to define the design specifications, includingthe numbers of members, types of joints, and categoriesof components.Step 2 Atlas of Generalized Chains

According to the process of generalization(24) – (26),the corresponding generalized chains of existing SouthPointing Chariots can be obtained. The atlas of general-ized chains with the required numbers of links and jointscan be generated based on the algorithm of number syn-thesis or graph theory.Step 3 Atlas of Feasible Specialized Chains

Through the process of specialization(25), (26), specifictypes of members and joints are assigned to each general-ized chain available in Step 2 to obtain the correspondingatlas of feasible specialized chains subject to design re-quirements and constraints.Step 4 Atlas of Feasible Specialized Chains with Par-ticular Identities

Here, the axial direction to each revolute pair and con-nection characteristic to each non-revolute pair first areassigned. We identify the members of inputs/output andcombine the suitable type of the transmission part withthe atlas of feasible specialized chains derived in Step 3 to

generate the atlas of feasible specialized chains with par-ticular identities.Step 5 Atlas of Designs

According to the requirements of motion and functionof the mechanical devices, the corresponding schematicformats are particularized from the atlas of feasible spe-cialized chains with particular identities to establish theatlas of all designs.

6. Design Examples

In what follows, we demonstrate the feasibility of theproposed design procedure shown in Fig. 3 by three ex-amples. In different dynasties of ancient China, differentdesigns of the South Pointing Chariot were invented.Example 1

In the process of mechanism design, engineers alwaysaccomplish the motion and function requirements withfewer links. Since the South Pointing Chariot is composedof two inputs, an output and a frame, the numbers of linksare four at least. Therefore, we synthesize the differential-type South Pointing Chariots with four links as follows:Step 1 Specifications

The types of members are open in this case. The de-sign specifications are:

1. The numbers of links of the passive feedbackmechanism are four.

2. The degrees of freedom are two.3. The types of mechanical components are linkages,

gears, ropes, pulleys, and rollers.Step 2 Atlas of Generalized Chains

For a planar mechanism with two degrees of freedom(FP = 2) and four links (NL = 4), the number of joints is 4(NJ = 4; 1 joint with two degrees of freedom and 3 jointswith one degree of freedom) or 5 (NJ = 5; 3 joints withtwo degrees of freedom and 2 joints with one degree offreedom). Figure 4 (a) and (b) shows the atlas of general-


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(a) NL =4, NJ =4 (b) NL =4, NJ =5

Fig. 4 Atlas of generalized chains (Example 1)

ized chains with four links and four and five joints, respec-tively.Step 3 Atlas of Feasible Specialized Chains

Once the atlas of generalized chains is obtained, allpossible specialized chains can be identified according tothe following steps:

1. For each generalized chain, identify the frame linkfor all possible cases.

2. For each case obtained in Step 1, assign revolutepairs.

3. For each case obtained in Step 2, assign non-revolute pairs.

The members and the joints must be assigned subjectto the following design requirements and constraints:Frame (KF)

a. One of the links in each generalized chain must bethe frame.

b. A frame must not be included in a three-bar loopin the chain.

c. A frame must be a multiple link in order to havetwo input members and one output member.Revolute Pair (JR)

a. There must be NL−1 revolute pairs.b. Any joint incident to the frame must be a revolute

pair.c. Every link must have at least one revolute pair.d. There can be no loop formed exclusively by revo-

lute pairsRolling Pair (JO)/ Gear Pair (JG)

a. A binary link can not have two gear pairs or rollingpairs.

b. A ternary link can only have two gear pairs orrolling pairs.

c. There can be no three-bar loop formed exclusivelyby gear pairs.

After assigning all types of joints and members, weobtain the atlas of feasible specialized chains as shown inFig. 5.Step 4 Atlas of Feasible Specialized Chains with Partic-ular Identities

In this step, the axial directions of revolute pairs andthe characteristics of non-revolute pairs are identified firstaccording to the following points:

(a) (b)

Fig. 5 Atlas of feasible specialized chains (Example 1)

1. Identify the superscript “V” or “H” to each revo-lute pair.

2. There must be at least one revolute pair in the hor-izontal direction.

3. The subscript of non-revolute pairs is identified as“B” to represent the axial directions of the two adjacentmembers that are perpendicular to each other.

4. The subscript of non-revolute pairs is identified as“SI” or “SE” to represent the axial directions of the twoadjacent members that are horizontal. Here, “I” or “E”indicates the two gears (rollers) adjacent to a gear (rolling)pair can be internal or external.

Different designs are obtained by assigning differentmembers as the two inputs and the output in the special-ized chains. The inputs and the output are identified asfollows:Input

a. The input link has to be adjacent to the frame.b. Input 1 must not be adjacent to input 2.

Outputa. The axial direction of the output link has to be ver-

tical to the ground.b. There can be no loop formed exclusively by the

two inputs and the output.Finally, the type of transmission part in all the fea-

sible specialized chains is considered. This connects thetwo inputs and the passive feedback mechanism. Gener-ally, the simplest solution is to connect directly. Since thegear train system of the South Pointing Chariots may add acompound gear as the transmission part, the South Point-ing Chariots with frictional components have two choices:one is to add a compound roller and the other is to connectwith pulleys and ropes. As a result, we obtain the atlasof feasible specialized chains with particular identities asshown in Fig. 6.Step 5 Atlas of Designs

Graphically, particularization is the reverse processof generalization. However, we must notice that the ro-tational direction of the output should be opposite to thechariot when turning left or right. Figure 7 shows the atlasof designs through particularization, and we obtain 8 fea-sible design concepts of the differential-type South Point-ing Chariots with four links. The design in Fig. 7 (d) is


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(a) (b) (c) (d)

(e) (f) (g) (h)

Fig. 6 Atlas of feasible specialized chains with particular identities (Example 1)

(a) (b) (c) (d)

(e) (f) (g) (h)

Fig. 7 Atlas of designs (Example 1)

designed by Yan(12).Example 2

Available literature indicates that most of the feasiblemechanisms of the differential-type South Pointing Char-iots are gear train systems with five links. According toarcheological research, it seems that gears were appliedto some mechanical devices in the period of Qin Dynasty(221–206 BC) and Han Dynasty (206 BC–220 AD). Fur-thermore, many agricultural machinery used gears in an-cient China. Hence, most scholars agree that the SouthPointing Chariots were designed with gear train systemsin ancient China. Therefore, the goal of this design exam-ple is to generate all possible designs of the differential-type South Pointing Chariots with five links and with geartrain systems. The design specifications are as follows:

1. The numbers of links of the passive feedback

mechanism are five.2. The degrees of freedom are two.3. The types of mechanical components are links and

gears.Following the same design procedure as shown in

Fig. 3 and described in Example 1, we can obtain the cor-responding atlas of generalized chains, atlas of feasiblespecialized chains, and atlas of feasible specialized chainswith particular identities. Figure 8 shows the process ofthe reconstruction design for the required South PointingChariots. Figure 9 shows the atlas of 18 feasible designsin which Fig. 8 (d-1) is Lanchester’s design(7), Fig. 8 (a-4) and (d-4) is Lu’s designs(11), Fig. 8 (d-3) is Yan’s de-sign(12), Fig. 8 (a-5) is Yang’s design(14), and Fig. 8 (a-3),(b-1), and (b-2) is Hsieh’s designs(18).


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Fig. 8 Reconstruction design (Example 2)

Example 3In ancient China, the developments of laborsaving de-

vices were very mature and full of various applications, es-pecially the rope-and-pulley mechanisms. Winches werevery popular and widely used before the Qin Dynasty.Moreover, friction wheels have the function of trans-

mitting continuous rotational motion and the advantageof being simple in structure. Here, we synthesize thedifferential-type South Pointing Chariots with ropes, pul-leys, and friction wheels in this example. The design spec-ifications are as follows:

1. The numbers of links of the passive feedback


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mechanism are five.2. The degrees of freedom are two.3. The types of mechanical components are ropes,

pulleys, and friction wheels.For practical applications, the two friction wheels ad-

jacent to a rolling pair are only with the external connec-tion. We apply the rope-and-pulley as the transmissionpart. Following the same design procedure as shown inFig. 3 and presented in Example 1, we obtain the corre-sponding atlas of generalized chains, atlas of feasible spe-cialized chains, and atlas of feasible specialized chains

with particular identities as shown in Fig. 10. Finally,we obtain 4 feasible designs through the particularizationprocess as shown in Fig. 11 in which Fig. 10 (f-1) is Chen’sdesign(19).

7. Conclusions

The most difficult task of the reconstruction researchon ancient machinery is to create the reconstruction de-signs. According to the historical literature of South Point-ing Chariot in ancient China, the interior mechanisms arestill mysteries. Consequently, this study systematically


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Fig. 10 Reconstruction design (Example 3)

provides a different view for the structural synthesis of thelost ancient machinery.

In summary, novel representations for joints andmembers are proposed. This not only shows different de-signs with the same topological structures in the analy-sis process, but also indicates the four parts of the SouthPointing Chariot. The design requirements and constraintsof South Pointing Chariots are defined according to thetopological structures of the existing designs. A system-atic approach is presented for synthesizing all possible de-sign concepts of the differential-type South Pointing Char-iots that are consistent with available mechanical membersof the subject time period. Finally, three design examplesare provided to design the differential-type South PointingChariots based on the required design specifications. Theresult of this work provides a novel approach for the studyof lost ancient machinery, especially the South Pointing

Chariots.

Acknowledgements

The authors are grateful to the financial support of theNational Science Council (TAIWAN, ROC) under grantsNSC 91-2212-E006-089, NSC 92-2212-E006-019, andNSC 93-2212-E006-003.

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