**HP 42S & DM 42 Linear Progression of a Slider Crank**

**Introduction**

Welcome to first post of 2020! In today's post, the program CRANK will calculate the following:

* Maximum (xMAX) and Minimum (xMIN) slider displacement of a slider crank using linear progression

* Connecting rod angle, slider displacement, the slider's velocity, and slider's acceleration given the crank angle

Input values are:

* Connecting rod length (L)

* Crank radius (R)

* Vertical slider offset (E)

* Current speed of the crankshaft, in revolutions per minute (RPM)

* Crank angle (θ)

The program does not dictate units of measure (such as inches, millimeters, etc). However, all angles are measured in degrees and the program sets the calculator to Degrees mode.

**HP 42S/DM42 Program: Linear Progression of a Slider Crank**

00 { 317-Byte Prgm }

01▸LBL "CRANK"

02 DEG

03 CLMENU

04▸LBL 00

05 "LNGTH"

06 KEY 1 GTO 01

07 "ANGLE"

08 KEY 2 GTO 02

09 "LIMITS"

10 KEY 3 GTO 03

11 "∡ v a"

12 KEY 4 GTO 04

13 "EXIT"

14 KEY 5 GTO 05

15 MENU

16▸LBL 10

17 STOP

18 GTO 10

19▸LBL 01

20 "ROD LGTH:"

21 PROMPT

22 STO 01

23 "RADIUS:"

24 PROMPT

25 STO 02

26 "OFFSET:"

27 PROMPT

28 STO 03

29 "RPM:"

30 PROMPT

31 STO 04

32 "DONE"

33 AVIEW

34 GTO 00

35▸LBL 02

36 "ANGLE:"

37 PROMPT

38 STO 05

39 "DONE"

40 AVIEW

41 GTO 00

42▸LBL 03

43 RCL 03

44 RCL 02

45 RCL+ 01

46 ÷

47 ASIN

48 COS

49 RCL 02

50 RCL+ 01

51 ×

52 "xMAX="

53 ARCL ST X

54 AVIEW

55 STOP

56 RCL 03

57 RCL 01

58 RCL- 02

59 ÷

60 ASIN

61 COS

62 RCL 01

63 RCL- 02

64 ×

65 "xMIN="

66 ARCL ST X

67 AVIEW

68 STOP

69 GTO 00

70▸LBL 04

71 PI

72 RCL× 04

73 30

74 ÷

75 STO 07

76 RCL 05

77 SIN

78 RCL× 02

79 RCL+ 03

80 RCL÷ 01

81 ASIN

82 STO 06

83 "CRANK ∡="

84 ARCL ST X

85 AVIEW

86 STOP

87 RCL 02

88 RCL 05

89 COS

90 ×

91 RCL 01

92 RCL 06

93 COS

94 ×

95 +

96 "POS="

97 ARCL ST X

98 AVIEW

99 STOP

100 RCL 05

101 RCL+ 06

102 SIN

103 +/-

104 RCL 06

105 COS

106 ÷

107 RCL× 07

108 RCL× 02

109 "VELOCITY="

110 ARCL ST X

111 AVIEW

112 STOP

113 RCL 05

114 RCL+ 06

115 COS

116 +/-

117 RCL 06

118 COS

119 ÷

120 RCL 05

121 COS

122 X↑2

123 RCL× 02

124 RCL 06

125 COS

126 3

127 Y↑X

128 RCL× 01

129 ÷

130 -

131 RCL 07

132 X↑2

133 ×

134 RCL× 02

135 "ACCEL="

136 ARCL ST X

137 AVIEW

138 STOP

139 GTO 00

140▸LBL 05

141 CLMENU

142 EXITALL

143 RTN

144 END

Download: https://drive.google.com/open?id=1z0Htza_-quZ4VLIddSqTg54pM_54_uFP

**Instructions**

1. Run CRANK by pressing XEQ CRANK

2. Enter rod length (ROD LGTH), crank radius (RADIUS), offset (OFFSET), and turning speed (RPM) by pressing the LNGT submenu. After all the input values are entered, you will see a DONE message. Use the [R/S] key to enter values.

3. To enter a crank angle, choose the ANGL submenu. Enter the crank angle. After the angle has been entered, you will see a DONE message.

4. Calculate the maximum and minimum slider displacements by choosing the LIMIT submenu.

5. Calculate the rod angle, position, velocity, and acceleration by the ∠ v a submenu.

6. You can renter any of the inputs at any time.

7. To exit the program, press EXIT.

**Example**

(Fix 4 Setting)

Rod length: 8 in

Crank radius: 2 in

Offset: 1.3 in

RPM: 5000 RPM

Crank Angle: 15°

Results:

xMAX=9.9151

xMIN=5.8575

CRANK ∠=13.1326

POS=9.7226

VELOCITY=-507.0277

ACCEL=-634,997.3666

Crank Angle: 20°

(xMAX and xMIN remain the same)

CRANK ∠=14.3595

POS=9.6295

VELOCITY=-610.0807

ACCEL=-600,369.9284

Source:

"Linear Progression of Slide Crank" HP 65 Machine Pac-1. Hewlett Packard. 1975

Eddie

All original content copyright, © 2011-2020. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

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